Recent Advances in Electrical Engineering
st
Abstract: This paper proposes a static synchronous compensator (STATCOM) for single-phase load compensation in three-phase power distribution system. Each main circuit arm of the STATCOM uses cascade multilevel full H-bridge (FHB) converter. The three main STATCOM arms are delta-connected, which allows independent operation for load balancing and power factor correction. A feedforward compensation scheme derived from the symmetrical components method is employed for the STATCOM to meet fast response requirement. The STATCOM is built and simulated in the MatLab/SimuLink program. Simulation results verify the effectiveness of the proposed STATCOM.
Key-words: Single-phase load compensation, FHB converter, STATCOM, Symmetrical components method,
Simulation.
A large capacity of single-phase load, such as electrical railway system, in a three-phase, threewire electric power distribution system absorbs unbalanced load current from the power source. The unbalanced load current produces additional system losses in the distribution system and creates unbalanced voltage drop on the power distribution line. The unbalanced voltage drop results in unbalanced voltage on the load bus and affects other sensitive loads connected at the bus. Hence, the unbalanced load current should be compensated for keeping good power quality.
Since 1970s, static var compensators (SVCs) are widely used in electric power industries for unbalanced load compensations. An SVC with delta-connected configuration and phaseindependent operation ability can be used to balance unbalanced load and correct load power factor to unity at the same time [1-2]. Recently, due to rapid development of high power switching elements such as IGBTs and IGCTs, static synchronous compensator (STATCOM) has been recognized as next-generation compensator [3-6]. Compared to existing SVCs, STATCOM has quicker response time and compact structure. Many types of converters can be used to construct the main circuit of the STATCOM. Among them, due to modular structure and lower voltage stress, cascade full Hbridge (FHB) converter is very suitable for main circuit of the STATCOM in high power and high voltage applications [7-12].
In the paper, a delta-connected STATCOM with cascade multilevel FHB converter is proposed for real-time single-phase load compensation. A simple and effective feedforward compensation scheme is introduced for the STATCOM. The
STATCOM is constructed and simulated by using the MatLab/SimuLink program. Simulation results show that the proposed STATCOM has very quick response time and satisfactory compensation effect.
Figure 1 shows a power distribution system with a single-phase load and the proposed STATCOM with delta-connected configuration. Each arm of the
STATCOM consists of an internal voltage source
V ST and a reactor X ST . In this paper, the STATCOM is treated as purely reactive power load. The three main circuit arms of the STATCOM are regulated independently for the single-phase load compensation. The active power and reactive power inputs of each STATCOM arm in Fig. 1 are expressed by (1) and (2), respectively [13].
P
ST
Q
ST
 

V V
ST
L sin
V L
X
( V L V ST cos

ST )
X
ST

ST (1)
(2)
An indirect regulation method is used for the
STATCOM in the reactive power control. For the need of capacitive compensation, the controller of
ISBN: 978-1-61804-299-6 119

Recent Advances in Electrical Engineering the STATCOM regulates the power angle

ST to negative value to absorb active power from system according to (1). The active power input charges the dc-link capacitors and boosts the dc-link voltages.
When the dc-link voltages increase, the internal voltage V ST rises too. With the power angle regulation, the STATCOM absorbs capacitive reactive power according to (2). The power angle goes back to zero when the reactive power input reaches the desired value. Phase-independent operation of the three STATCOM arms is achieved with the delta-connected structure. Hence, unbalanced load current can be compensated easily like a traditional SVC.
V
S a
V
L a
V b
S
V
S c
V
L b
V
L c
Singlephase
Load
Z
S without even order harmonic component. Equation
(4) shows the amplitude of each harmonic order in equation (3). v ST (
 t )

4 V dc n
 n



1
[cos( n

1
 n

2
 n

3
)
 cos( n

4
 n

5
)]sin(

)
(3)


4 V dc n

[cos( n

1
 n

2 cos( n

4
 n

5 n

 n

3
)
(4) v L ab

5 V dc v
ST ab
*
ST v bc
0

ST

2


X
ST
ST
I ab
+ v
ST ab 1
-
+ v
ST ab 2
-
V
ST ab
  ST ab
V
L ab

0

+ v
ST ab 3
-
+ v
ST ab 4
-
C ab 1
C ab 2
C ab 3
C ab 4
V
L bc
L
V ca
+ v
ST ab 5
-
C ab 5
Arm a-b
Fig. 1 A power distribution system with a singlephase load and the proposed STATCOM
A staircase modulation scheme is employed for the 11-level STATCOM in Fig. 1. Figure 2 shows each level and internal voltage waveforms of the
STATCOM arm a-b with five FHB cells in Fig. 1
[14]. The internal voltage v ST waveform. These switching angles,

1
~

5
, should be selected for minimizing the harmonics generated.
The internal voltage v
ST can be represented as a
Fourier series, as shown in (3). In (3), n is the harmonic order of the v
ST , where n

1,3,5, 7,...
.
Ideally, the harmonic orders contain only odd orders
-5 V dc v
ST ab 5 
5
 
5

5
 
5 v
ST ab 4 
4 4


2
4
 
4 v
ST ab 3 v
ST ab 2

3 3
2
3
 
3


2 2 v
ST ab 1 
1

 
1
 
1

1
Fig. 2 Staircase modulated voltage waveforms of the
STATCOM arm a-b
In (4), taking n

1 obtains the fundamental component, which relates the relationship of V
ST and the dc-link voltage V dc
. The fundamental component H (1) consists of dc-link voltage V dc five switching angles,

1
to

5
and
. To eliminate the specified harmonic orders, 3 th , 5 th , 7 th , and 9 th
, a harmonic minimizing method is employed by using
(5) [15-16]. c
  cos(

2
)
   cos(

4
)
 
5
 

1
 
2
 
3
 
4
 
5

0

1
 cos(5

2
)
 
3
 cos(5

4
)
 
5

0

1
 cos(7

2
)
 
3
 cos(7

4
)
 cos(7

5
)

0
  cos(9

2
)
   cos(9

4
)
 
5

0
(5)
Where: 0
  
1
 
2
 
3
 
4
 
5

90

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Recent Advances in Electrical Engineering
Solving (5) by using Newton-Raphson’s method obtains the needed switching angles,

1
= 6.3
 ,

2
= 16
 ,

3
= 30.9
 ,

4
= 41.9
 ,

5
= 63.7
 .
Figure 3 shows the studied system with a threephase unbalanced load and a compensator for onsite load compensation. The compensator and the unbalanced load are represented by using admittances.
I a
S
V a
S
I a
L
V b
S
I b
S
I b
L
Y ab
L
Y bc
L
Y ca
L
I c
S
V c
S
I c
L
I c
ST
ST jB ca
I a
ST I b
ST jB
ST ab
B ST ab
* v
L
Unbalanced
Load
, , i
L
ST jB bc
ST
B bc
*
B ST ca
*
Compensation
Schemes
Compensator
Fig. 3 An unbalanced load and a compensator
Use of the symmetrical components method obtains a well-known feedforward compensation scheme for the compensator, as shown in (6) [1].
B
ST ab

B
L ab

( G
L ca

G
L bc
) 3
B ST bc

B L bc

( G L ab

G L ca
) 3 (6)
B ST ca

B L ca

( G L bc

G L ab
) 3
Assuming the single-phase load to be compensated is connected between the phase a-b , which simplifies (6) to (7). Multiplying both sides of (7) with line-to-line voltage of load bus yields (8).
The compensation scheme of the STATCOM is obtained in terms of load powers.
B ST ab

B L ab
B ST bc

G L ab
/ 3 (7)
B ST ca
 
G L ab
3
Q ST ab
*
 
Q L ab
Q ST bc
*
 
P L ab
/ 3 (8)
Q
ST ca
* 
P
L ab
/ 3
In (8), the compensation scheme detects the load powers and sends three reactive power compensation commands to the three STATCOM arms. The STATCOM is treated as purely reactive power load in steady state. Each arm power input of the STATCOM, which can be inductive or capacitive, is controlled independently according to the compensation scheme in (8). The line current of the STATCOM compensates the negative-sequence component and imaginary part of the positivesequence component of the load current. In this way, the source current is compensated to be balanced and unity power factor.
Figure 4 shows the block diagram of the proposed STATCOM controller in the paper. The control scheme using (8) calculates the needed reactive powers of the three STATCOM arms in real-time. Use of three PID feedback controllers regulates the reactive power inputs of the three
STATCOM arms, independently. The commands
 ST* ab,bc,ca
generate the gating signals according to Fig. 2 for switching elements in the three STATCOM arms.
With the controller regulation, the STATCOM completes the phase balancing and unity power factor correction of the single-phase load in realtime. v
L
, ,
PLL

, ,
Load Power and
Compensation
Scheme
Calculations
Q ST ab
*
Q ST bc
Q ST ca
*
*
+ -
+
-
PID

ST ab
*
PID

ST bc
*
PID

ST * ca
Switching
Patterns
Generator
+ -
Q
ST ab
Q
ST bc
Q
ST ca
Gating
Signals i
L v
L
STATCOM
Each Arm
Reactive Power
Detection i ST
, ,
Cascade
Multi-level
STATCOM and System
Fig. 4 The proposed STATCOM controller
A fast powers detection method is needed for real-time compensation of the single-phase load in
Fig. 4. Figure 5 shows the active and reactive powers calculation method for the STATCOM controller by using the single-phase q-d reference axis method. With the fast calculation method, the needed load powers for (8) and the reactive powers of the three STATCOM arms are calculated in realtime.
ISBN: 978-1-61804-299-6 121

Recent Advances in Electrical Engineering


2
( )

/2





2
( )

/2



Fig. 5 The powers calculation method
Figure 6 shows the simulation system constructed in the MatLab/SimuLink program for the effectiveness verification. In the simulation, a single-phase load is used in the testing. The Appendix lists the system parameters in the simulation. v a
S
X a
S v a
L i a
S a i a
L
CT
SW v b
S
X b
S v b
L i b
S
+
L v
ab b i b
L
PT
L
Z ab v c
S
X c
S v c
L i c
S c i b
ST i
ST
, , v L
, ,
L v ab i a
L i c
ST
Q ST ca i a
ST
Q ST ab
Compensation
Scheme and
Switching
Patterns
Generation
Gating
Signals
ST
Q bc
Fig. 6 Simulation system setup
The switch (SW) in Fig. 6 is closed at t=1.5 sec in the simulation. The transient and steady state responses of the system with the STATCOM compensation are observed. Figures 7 and 8 are the simulation results. Figure 7( a ) shows the load current response. Figure 7( b ) is the load current response. With the STATCOM compensation, the three-phase source current is corrected to balance with unity power factor in real-time. Figure 7( c ) shows the synthesized line current of the STATCOM for reference. Figures 7( d ) and 7( e ) show the active and reactive powers to the load and from the power source, respectively. The reactive power demand of the load is compensated very quickly by the
STATCOM. This also confirms the compensation effect.
20
10
0 i a
L
-10
-20
3.00
v a
L / 6
3.01
i b
L i L c

0
3.02
3.03
3.04
3.05
Time(s)
3.06
(a) phasea load bus voltage ( v L a
3.07
3.08
3.09
3.10
) and load current
( i L )
15
7.5
i a
S
0.0
-7.5
-15 v
L a
/ 10 i
S b i
S c
3.00
3.01
3.02
3.03
3.04
3.05
Time(s)
3.06
(b) phasea load bus voltage ( v
L a
3.07
3.08
3.09
3.10
) and three-phase source current ( i S )
20
10 i b
ST i c
ST
0
-10 i a
ST
-20
3.00
3.01
3.02
3.03
3.04
3.05
Time(s)
3.06
3.07
3.08
(c) line current of STATCOM ( i
ST a,b,c
)
3.09
1.5
1.0
P
L
3.10
0.5
Q
L
0.0
-0.5
3.00
3.01
3.02
3.03
3.04
3.05
Time(s)
3.06
3.07
3.08
(d) power ( P
L , Q
L ) to the load
1.5
1.0
P
3
S

0.5
3.09
3.10
0.0
-0.5
3.00
3.01
3.02
3.03
Q
S
3

3.04
3.05
Time(s)
3.06
3.07
3.08
3.09
3.10
(e) power ( P
3
S

, Q
S
3

) from the source
Fig. 7 System response with the STATCOM compensation
Figure 8 shows the compensation response in the STATCOM. Fig. 8( a ) is the internal voltage responses of the three STATCOM arms. The
STATCOM goes into unbalanced operation when the single-phase load is switched-in. This is also shown in Fig. 8( b ). It is observed that the unbalanced operation of the STATCOM causes
ISBN: 978-1-61804-299-6 122

Recent Advances in Electrical Engineering harmonic currents in the three main circuit arms of the STATCOM. The resulting harmonic currents will flow into the system and affect the electric power quality. In practical applications, adequate filters should be designed to eliminate the harmonic currents. Increasing the cascade number of the FHB cells in the STATCOM main circuit can significantly reduce the harmonic currents generated. Figures 8(c)
- (e) show other responses in the STATCOM for the single-phase load compensation.
The simulation results in Figs. 7 and 8 clearly show that the proposed STATCOM in the paper is very suitable for single-phase load compensation. v
ST ab v
ST bc v
ST ca
200
100
0
-100
-200
3.00
3.01
3.02
3.03
3.04
3.05
Time(s)
3.06
3.07
3.08
(a) each arm internal voltage ( v
ST ab,bc,ca
)
3.09
15 i
ST bc
7.5
i ST ab
0.0
-7.5
i ST ca
-15
3.00
3.01
3.02
3.03
3.04
3.05
Time(s)
3.06
3.07
(b) each arm current ( i
ST ab,bc,ca
)
3.08
3.09
3.10
3.10
1.0
0.0
-1.0
1.0
0.0
-1.0
1.0
0.0
-1.0
3.00
3.01
3.02
3.03
3.04
3.05
Time(s)
3.06
3.07
3.08
(c) each arm compensation command ( Q
ST *
, ,
5.0
3.09
3.10
)
0.0
-5.0
5.0
0.0
-5.0
5.0
0.0
-5.0
3.00
3.01
3.02
3.03
3.04
3.05
3.06
3.07
3.08
Time(s)
(d) each arm power angle command (

ST *
, ,
3.09
)
3.10
40
30
20
40
V
ST
30
20
V ST
40
30
V
ST
20
3.00
3.01
3.02
3.03
3.04
3.05
Time(s)
3.06
3.07
3.08
3.09
3.10
(e) dc-link voltages of FHB cells in STATCOM arms.
Fig. 8 STATCOM compensation response
A delta-connected STATCOM employing cascade multilevel full H-bridge converter for real-time single-phase load compensation in three-phase power distribution system has been studied in the paper. A simple and effective feedforward compensation is proposed for the STATCOM. The computer simulation results by using the
MatLab/SimuLink program show that the function of the proposed STATCOM is quite satisfactory. The simulation result also show some undesired phenomena. During the STATCOM compensation, unbalanced operation of the STATCOM induces unbalanced harmonic currents in the three
STATCOM arms. In practical applications, harmonic filters should be designed for enhancement of electric power quality.
References:
[1] T. J. E. Miller, Reactive Power Control in
Electric System , Wiley & Sons, New York,
1982.
[2] L. Gyugyi, R. A. Otto, and T. H. Putman,
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“Average power balancing control of a
STATCOM based on the cascaded H-bridge
PWM converter with star configuration,” IEEE
Transactions on Industry Applications, vol. 50, no. 6, pp. 3893-3901, 2014.
ISBN: 978-1-61804-299-6 123

Recent Advances in Electrical Engineering
[5] W. Song, and A. Q. Huang, “Fault-tolerant design and control strategy for cascaded Hcurrent,”
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IEEE Transactions on Power
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[15] S. Du, J. Liu, J. Lin, and Y. He, “A novel DC voltage control method for STATCOM based on hybrid multilevel h-bridge converter,” IEEE transformerless energy storage system based on a cascade multilevel PWM converter with star configuration,” IEEE Transactions on Industry
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Appendix: Simulation Parameters
System side:
V ll
S 
190 V , f
S


1
 
2

60 Hz, X
S a,b,c
STATCOM side:
C ab 1,2,3,4

C bc 1,2,3,4


C ca 1,2,3,4
 

0 1

, Z
L ab

2, 200

,
 
4
 

8 6
ST
, ,
 

1.885

ISBN: 978-1-61804-299-6 124