Download A. Negative-Sequence Reactive-Power Control

International Journal of Electrical, Electronics and Computer Systems (IJEECS)
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MODELING AND SIMULATION OF PWM BASED STATCOM
FOR REACTIVE POWER CONTROL
1
N.Rajkumar, 2C.Sharmeela
1
Student, Institute for Energy Studies, Dept. of Mechanical Engg., College of Engineering Guindy,
2
Assistant Professor (Sr. Gr) in EEE, Department of Chemical Engg. A.C.Tech.,
Anna University, Chennai, India
Email : [email protected], [email protected]
Abstract—This dissertation is dedicated to Modeling and
Simulation of STATic synchronous COMpensator
(STATCOM) for Reactive Power Control. Among Flexible
AC Transmission System (FACTS) controllers, the
STATCOM has shown feasibility in terms of cost
effectiveness in a wide range of problem solving abilities
from transmission to distribution levels. The Modular
Multilevel Cascaded Converters (MMCCs) with separated
Direct Current (DC) capacitors is the most feasible
topology for use as a power converter in the STATCOM
applications. To be able to operate in a high voltage
application, a large number of DC capacitors are utilized
in a MMCC based STATCOM. All DC capacitor voltages
must be balanced in order to avoid overvoltage on any
particular link. MMCC based on Single Delta Bridge Cells
(SDBCs) to a STATCOM, particularly for reactive-power
control. SDBC is categorized by cascade connection of
multiple single phase H-bridge (or full bridge) converter
cells per leg, hence simplifying flexible circuit design and
low voltage steps. Modeling and Simulation of a 100V
5kVA Pulse Width Modulated (PWM) STATCOM based
on the SDBC using MATLAB/Simulink, with focus on the
operating principle and performance. Simulation results
show that it can control positive sequence reactive power,
negative sequence reactive power and also low frequency
active power.
Index Terms— STATCOM, multilevel converters, MMCC,
reactive power, positive –sequence reactive power,
negative-sequence reactive power.
I. INTRODUCTION
The Family of MMCC is expected as one of the nextgeneration power converters suitable for high-voltage or
medium-voltage applications without line-frequency
transformers [1] – [21]. From power-circuit and
converter-cell configurations, it can be classified into the
following [2]:
1) Single Star Bridge Cells (SSBCs)
2) Single Delta Bridge Cells (SDBCs)
3) Double Star Chopper Cells (DSCCs)
4) Double Star Bridge Cells (DSBCs)
The term “bridge cell” is a single-phase H-bridge (or full
bridge) converter, and the “chopper cell” is a
bidirectional chopper consisting of a dc capacitor and
two insulated-gate bipolar transistors. SSBC is a STAtic
Synchronous COMpenstator (STATCOM) for voltage
regulation [11], [13] and battery energy storage systems
[14], [15]. However, without significantly increasing the
converter-cell count, the SSBC-based STATCOM
cannot draw any negative sequence reactive power
because it has no circulating current. The SDBC, DSCC
and DSBC are suitable for STATCOM for negative
sequence reactive power control because they have the
circulating current(s) that flow inside. Converter-cell
count required for the DSCC is four times of that for the
SSBC.
The authors of this paper have described the DSCC
acting as a STATCOM with focus on control and
performance [20], [21]. Attention has been paid to
STATCOMs based on the SDBC [8]-[10]. The SDBC
seems to be a better choice than the DSCC from a
practical point of view because the converter-cell count
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required for the SDBC is only 1.7 (=√3) times of that for
the SSBC [2]. The authors of this paper have described
the SDBC acting as STATCOM with experimental
verification using down scaled model of 100, 5kVA.
Experimental results verify that it can control not only
positive-sequence reactive power but also negative
sequence reactive power and low-frequency active
power at the same time. However, no simulation
verification has been made in the literature [1].
The aim of this paper is to provide modeling and
simulation verification of an SDBC-based pulse widthmodulated (PWM) STATCOM for reactive-power
control. This paper proposes a control method that is
characterized by forming a feedback loop of the
circulating current among the delta-connected clusters,
leading to stable dc-mean voltage control of all the dc
capacitors. This paper models and followed by
simulation verification using a downscaled model rated
at 100 V and 5 kVA. Simulation results verify that it can
control positive-sequence reactive power, negative
sequence reactive power and low-frequency active
power at the same time.
II. MMCC-SDBC CONFIGURATIONS
Fig. 1 shows two kinds of SDBC-based STATCOM.
The SDBC is characterized by easily increasing the
voltage and current ratings without using line frequency
converter transformers.
III. CIRCUIT CONFIGURATION OF THE
SDBC
A. Circuit Configuration
Fig. 2 shows the detailed circuit configuration of the
100V 5kVA STATCOM used in MATLAB/Simulink.
Each cluster of the SDBC consists of cascade
connection of three bridge cells (i.e., single-phase fullbridge PWM converters), and the three clusters are
connected in delta configuration via a single coupled
inductor L.
The SDBC is connected to three-phase ac mains of
100V (line to line in rms) via a three-phase ac-link
inductor Ls that corresponds to the leakage inductance
of the grid transformer in Fig. 1(a). Here, vuv, vvw, and
vwu are the cluster voltages, iuv, ivw, and iwu are the
cluster currents, and p and q are the instantaneous active
and reactive powers at the PCC.
The following relations exist between the compensating
currents and the cluster currents. The compensating
currents and the supply currents are the same in Fig. 3
because no load (arc furnace) is connected.
iu=iuv–iwu
iv=ivw–iuv
iw=iwu−ivw.
(1)
Fig. 1(a) shows a 22-kV/33-kV system with a grid
transformer. Each cluster of the SDBC is connected in
delta configuration via a single coupled inductor. The
leakage inductance of the transformer works as ac-link
inductors between the grid and the SDBC.
Fig. 1(b) shows a 6.6-kV system with no grid
transformer. Each cluster of the SDBC is connected via
three noncoupled inductors. The SDBC can be
connected directly to the 6.6-kV grid because the
noncoupled inductors work as ac-link inductors.
Fig. 2 Circuit configuration of the 100V 5kVA MMCC
SDBC PWM STATCOM
Fig. 1 SDBC-based STATCOM. (a) 22-kV/33-kV
system with a grid transformer. (b) 6.6-kV system with
no grid transformer
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Fig. 3 Coupled inductor used
Let the circulating current flowing inside the deltaconnected clusters be iZ. It is defined as
iZ 
1
(iuv  ivu  iwu )
3
(2)
B. Simulation Parameters Used
DC Capacitor of Bridge Cell
C
164 mF/ 0.9
F
DC Capacitor Voltage
Reference
V*C
60 V
Unit Capacitance Constant
H
53 ms/2.9 s
Carrier frequency
fc
2 kHz
Equivalent Switching
frequency
6fc
12 kHz
AC Link inductor
Ls
0.5 mH
(8%*)
Coupled inductor
L
27 mH
(37%*)
*% inductance is on a three phase, 100V 5kVA and
50Hz base
Table I summarizes the simulation parameters of the
SDBC which will be used in simulation later on.
Each carrier frequency of phase-shifted PWM for bridge
cells was set as f C = 2 kHz. The command of each dc-
TABLE I Simulation Parameters
*
Description
Rating
capacitor voltage was set as VC = 60 V.
Rated Capacity
5kVA
The dc capacitor was set as either C= 16.4 mF (H = 53
ms) or C = 0.9 F (H = 2.9 s). The ac-link inductor and
the coupled inductor were set as LS = 0.5 mH (8%) and
Rated Line to Line rms
voltage
Vs
100V
Rated Line Frequency
ω/2∏
50 Hz
Rated Line Current
I
29 A
Rated Cluster Current
2I/√3
34 A
L = 2.3 mH (37%), respectively.
C. MATLAB/SIMULINK Model Development
As shown in Fig 4(a) to 4(d), MATLAB/SIMULINK
R2010a used to Model a Circuit configuration of 100V
5kVA MMCC SDBC PWM STATCOM and
MATLAB/SIMULINK developed models shown in Fig
4(a) to 4(d).
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Fig. 4(a) MATLAB/SIMULINK Modeling of Circuit configuration of 100V 5kVA MMCC SDBC PWM STATCOM
Fig. 4(b) MATLAB/SIMULINK Modeling of u-phase
H-Bridges circuit
Fig. 4(c) MATLAB/SIMULINK Modeling of v-phase
H-Bridges circuit
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Here,
vCu , vCv , vCw ,and v C are instantaneous values
containing both ac and dc components. It is desirable to
extract
only
the
dc
components
(i.e.,
(vCu ) dc , (vCv ) dc , (vCw ) dc and (vC ) dc because the
existence of the ac components deteriorates the
controllability.
Fig. 4(d) MATLAB/SIMULINK Modeling of w-phase
H-Bridges circuit
IV. CONTROL METHODS OF MMCCSDBC BASED PWM STATCOM
Fig. 5 shows the MATLAB/SIMULINK Model -block
diagram of the dc-capacitor voltage control. Voltage
control of the nine floating dc capacitors in Fig. 2 can be
divided into the following:
1) cluster-balancing control;
2) circulating-current control;
3) individual-balancing control.
A. Cluster-Balancing Control
Fig. 5(a) shows the MATLAB/SIMULINK Modelblock diagram of the cluster-balancing control. The
voltage major loop forces the average voltage of each
cluster, namely, vCu , vCv and vCw , to follow the average
voltage of the three clusters
v C where they are defined
as
1
1
 vCju ; vCv  3  vCjv
3
v  vcv  vcw
1
vcw   vCjv ; vc  cw
3
3
vCu 
(3)
Fig. 5 MATLAB/SIMULINK Model-Block Diagram of
dc-capacitor voltage control. (a) Cluster-balancing
control. (b) Circulating-current control. (c) Individualbalancing control.
The following methods can be utilized to extract the dc
components:
1) the method using a low-pass filter [11]
2) the method using a feed forward control;
3) the method using a moving-average filter of 100 Hz
[10]
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The last method is adopted in this project. Note that
sin(ωt +π/6) in Fig. 5(a) is in phase with Vuv.. When
*
(VC)dc > (VCu)dc the product of Vuv and iZ ( iZ ) forms
positive active power because iZ contains the same
B. Circulating-Current Control
Fig. 5(b) shows the MATLAB/SIMULINK Model-block
diagram of the circulating-current control. The current
*
minor loop forces iZ to follow its command iZ ,
producing the voltage command V*A that is common to
the three clusters.
component as Vuv. As a result, an amount of active
power flows into the u-phase cluster, thus leading to
increasing (VCu)dc. On the other hand, the product of Vuv
and iZ forms negative active power when (VC) dc < (VCu)
dc, thus leading to decreasing (VCu) dc
Hence, the sum of the voltage commands is equal to
zero. This means that no interference occurs between the
individual balancing control and the circulating-current
control.
D. Active-power, Reactive-Power, and Overall
Voltage Controls
C. Individual-Balancing Control
Fig. 5(c) shows the MATLAB/SIMULINK Model-block
diagram of the individual balancing control. It forms an
active power between the ac voltage of each bridge cell
and the corresponding cluster current. The voltage
commands
vB* ju , v B* jv , and v B* jw are given by
vB* ju  K 4(v Cu  vCju )iuv
vB* jv  K 4(v Cv  vCjv )ivw
(4)
vB* jw  K 4(v Cw  vCjw )iwu
The following equation is obtained from above equation:
3
v
j 1
*
B ju
3
 v
j 1
3
*
B jv
  vB* jw  0
j 1
Fig. 6 shows the MATLAB/SIMULINK Model-block
diagram of the active-power, reactive power, and overall
voltage controls, in which p*and q* represent the power
commands of p and q at the PCC.
The dc component of q*is adjusted to control positivesequence reactive power keeping the relation of p*= 0.
On the other hand, a couple of second-order components
(100 Hz) with the same amplitude but a phase difference
of 90◦ are superimposed on p* and q*, respectively, to
control negative-sequence reactive power. A lowfrequency component is superimposed on p* to control
active power, keeping the relation of q*= 0. The line toline voltage commands V*uv, V*vw, and V*wu are
determined by decoupled current control of the
compensating currents.
A voltage major loop intended for compensating the
converter loss is formed as shown in Fig. 6 which forces
(VC) dc to follow its command V*C.
(5)
Fig. 6 MATLAB/SIMULINK Model-Block Diagram of instantaneous active and reactive power controls, and
overall voltage control
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Fig. 7. MATLAB/SIMULINK Model-AC Voltage command of each bridge cell. (a) u-phase. (b) v-phase. (c) w-phase.
Fig. 7 shows the MATLAB/SIMULINK Model-AC
voltage command of each bridge cell. The voltage
command is normalized by each dc-capacitor voltage.
Then, it is compared with a triangular waveform having
a maximal value of 1 and a minimal value of −1 with a
carrier frequency of
where the initial phase was set as φ = 5π/6 so that the
amplitude of iuv has its maximal value.
Equation (6) and block diagram of instantaneous active
and reactive power controls, and overall voltage control
fC
give i*d and i*q as follows:
V. SIMULATION RESULTS AND
DISCUSSIONS
i d  5 cos(2t  56 )[ A]
*
i q  5 sin( 2t  56 )[ A]
*
In the present work, 100-V 5-kVA downscaled model
considered for the Modeling and Simulation of PWM
STATCOM for Reactive Power Control. The following
section explains the results obtained in the simulation.
(7)
where the dc component of i*d coming from the overall
Fig. 8 to 11 show the Simulation waveforms obtained
from the 100-V 5-kVA downscaled model. All the
Simulation waveforms were taken in a personal
computer (PC) through the MATLAB/Simulink R2010a
with different sampling frequencies.
i*v, and i*w as
Figs. 8, 9 and 11 had a sampling frequency of 100
kHz, and Fig. 10 had a sampling frequency of 20 kHz.
A. Negative-Sequence Reactive-Power Control
The instantaneous active and reactive power commands
in the three-phase circuit p* and q* are given by
voltage control is excluded from above equation.
Applying the inverse d−q transformation produces i*u ,
i u  41sin( t  6 )[ A]
*
i v  41sin( t  2 )[ A]
*
i w  41sin( t 
*
5
6
(8)
)[ A]
*
*
It is obvious from above equation that i u leads i w by
*
p  5 cos( 2t 
*
5
6
)[ kW ]
q  5 sin( 2t  56 )[ kVAr]
*
120o and i v by 240o, thus resulting in drawing the
negative-sequence reactive power from the ac mains.
(6)
Fig. 8 shows the Simulation waveforms when the
rated negative-sequence reactive power of 5 kVAr was
controlled. The cluster voltage Vuv is a seven-level
PWM waveform with a voltage step of 60 V (=V *C),
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containing much less harmonic voltages as well as much
less common-mode voltages than traditional two-level
voltage-source PWM converters. Since the carrier
frequency of each chopper cell is 2 kHz, the equivalent
switching frequency of the cluster is 12 kHz (2 kHz x 6).
The compensating currents iu, iv, and iw agree well with
their current commands.
The waveform of iu can be considered as a sinusoidal
waveform with a fundamental component of 50Hz. The
total harmonic distortion value of iu is low.The u-phase
cluster acts as an inductor because iuv lags Vuv by 90o
On the other hand, the v- and w-phase clusters act as a
capacitor because ivw leads Vvw by 90◦ and iwu leads Vwu
by 90o.
The dc-capacitor voltages VC1u, VC1v, and VC1w contain
both dc and ac components, in which the voltage control
regulates the dc component at 60 V. The ac component
consists of a second-order (100 Hz) frequency
component.
B. Active-Power and Reactive-Power Controls
Flicker compensation of arc furnaces requires to control
positive-sequence reactive power, negative-sequence
reactive power, and low-frequency active power at the
same time.
Fig. 9 Waveforms when a positive-sequence
capacitive reactive power of 1.7 kVAr, a negativesequence reactive power of 1.7 kVAr, and a10-Hz active
power of 1.7 kW were simultaneously controlled with a
condition of C = 16.4 Mf
As an example, p* and q* are given by
p *  1.7 sin(
t
5
)  1.7 cos( 2t 
q*  1.7 sin( 2t 
5
)[ kW ]
6
(9)
5
)  1.7[ kVAr]
6
Fig. 9 shows the Simulation waveforms when a positive
sequence capacitive-reactive power of 1.7 kVAr, a
negative sequence reactive power of 1.7 kVAr, and a 10Hz active power of 1.7 kW were simultaneously
controlled with a condition of C = 16.4 mF (H = 53 ms).
Since three different operating modes are intermixed,
the amplitude and phase of the currents are changing
dynamically as shown in Fig. 9. The amplitude of i Z in
Fig. 9 is one-third of that in Fig. 8 because the negative
sequence reactive power in Fig. 8 is reduced to one-third
of that in Fig. 8
Fig 8 Waveforms when the rated negative-sequence
reactive power of 5 kVAr was controlled with a
condition of C = 16.4 mF
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Fig 10 Waveforms when a 1-Hz active power of 5 kW
was controlled with a condition of C = 0.9 F
D. Transient-State Performance
Fig. 9 indicates that the amplitude of the 10-Hz
component is much larger than those of the 100-Hz
components because it is inversely proportional to ω or
ω0. Hence, larger capacitors are required to control lowfrequency active power.
It is clear from Fig. 11 that the STATCOM can achieve
fast negative-sequence reactive-power control without
delay time. However, the waveforms of VC1u, VC1v, and
VC1w show that a maximal voltage difference of 12V
(20%) occurs during the transient state. To increase the
capacitance of each dc capacitor is required to decrease
the voltage difference during the transient period.
C. Low-Frequency Active-Power Control
To control a 1-Hz instantaneous active power of 5 kW,
p*and q* are given by
p*  5 sin(
t
50
q*  0[kVAr]
)[ kW ]
(10)
Fig. 10 shows the Simulation waveforms in which each
of the dc capacitors was replaced with C = 0.9 F (H =
2.9 s). Both compensating and cluster currents form 1Hz envelopes as shown in Fig. 10, in which the
amplitude of the cluster currents was 1/√3 of that of the
compensating currents. Carefully looking into Fig. 10
reveals that the amplitudes of both cluster and
compensating currents when p*>0 are larger than that of
the currents when p*<0 due to the converter loss.
The relation of iZ = 0 always exists because no negativesequence reactive power was controlled. The dccapacitor voltages VC1u, VC1v, and VC1w contain both 1and 100-Hz components in which the former is much
larger than the latter.
Fig. 11 shows the Simulation waveforms when the
negative-sequence reactive power was increased from
2.5 to5 kVAr in 20 ms, kept constant for 20 ms, and
decreased from 5 to 2.5 kVAr in 20 ms with a condition
of C = 16.4 mF
VI. CONCLUSION
This paper has discussed Modeling and Simulation of
PWM based STATCOM using an MMCC-SDBC for
Reactive Power Control, with focus on operating
principle and performance, the simulation results
obtained from the 100V 5kVA downscaled model has
led to the following conclusions.
1) The SDBC has a capability to control negativesequence reactive power with the help of the circulating
current among the delta-connected clusters.
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2) Positive-sequence reactive power, negative-sequence
reactive power, and low-frequency active power can be
controlled simultaneously.
These conclusions suggest that the SDBC is applicable
to a STATCOM for Reactive Power Compensation.
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