A Simple Three-phase Model for Distributed Static
Series Compensator (DSSC) in Newton Power Flow
Reza Jalayer, Student Member, IEEE
Hossein Mokhtari, Member, IEEE
School of Electrical Engineering
Sharif University of Technology
Tehran,Iran
r_jalayer@ee.sharif.edu
School of Electrical Engineering
Sharif University of Technology
Tehran, Iran
mokhtari@sharif.edu
Abstract—Load flow problems have always been an important
issue in power system analysis and require proper modeling of
system components. In this regard Flexible AC Transmission
System (FACTS) controllers are modern devices that their
modeling specially the series type is a challenging topic. This
paper describes a three-phase model for Distributed Static Series
Compensator (DSSC) based on extending the Static Synchronous
Series Compensator (SSSC) model in Newton power flow. To
extend the SSSC model the following two differences must be
considered; three completely independent phases and the
existence of several modules in a DSSC system. Simulation results
on the IEEE 30-bus system and a five bus test system illustrates
the feasibility and performance of the proposed model in Newton
power flow algorithm.
lots of low power compensating modules with the same total
amount of compensation. Fig. 1 shows the DSSC distributed
units [6].
Keywords— disributed static series compensator (DSSC),
Newton power flow algorithm, flexible ac transmission system
(FACTS), static synchroous series compensatror (SSSC).
I. INTRODUCTION
R
APID development in the power electronics technology in
recent years is making Flexible AC Transmission system
(FACTS) as a promising solution to increase power system
controllability . FACTS controllers are high power (200~300
MVA) compensators in different types. Structurally, FACTS
controllers are divided into two main categories containing
thyristor-controlled and converter-based devices. The most
important converter-based FACTS controllers are Static
Synchronous Compensator (STATCOM) [2], Static
Synchronous Series Compensator (SSSC) [3], Unified Power
Flow Controller (UPFC) [4], and Distributed Static Series
Compensator (DSSC) [5]. A DSSC is an improved type of a
SSSC. Desired power flow control, increasing line thermal
capacity, improvement in power system stability and better
utilization of existing power lines are the main purposes of
series connected converter-based FACTS controllers (SSSC
and DSSC).
DSSC has been recently proposed to overcome SSSC's
problems. The main obstacles in wide applications of SSSC
and other FACTS controllers contain the non-promotable
capacity of the system leading to high investment at once,
expensive high-rated power electronics, enduring maintenance
and time consuming repair. The spread nature of the DSSC
system can overcome such problems by converting the lumped
and high power SSSC into a distributed system containing
Figure 1. Distributed compensation system [6].
A DSSC control system contains hundreds of modules
clamping on the line conductor with a specific distance from
each other (e.g. one mile) injecting a compensative voltage
directly into the line. Each module consists of a small rated
(10~20 KW) single phase inverter, a coaxial transformer also
called single turn transformer, related controls and a
communication link for modules coordination. The coaxial
transformer lets the module clamp mechanically and
electronically on the line conductor resulting in simple
installation and no more isolation problem. Fig. 2 demonstrates
inside a DSSC unit [5].
Figure 2. The structure of a DSSC unit [5].
The changes implemented in the DSSC system leads to the
following advantages,
1) The ability of developing compensative capacity
according to future load and demand
978-1-4244-2487-0/09/$25.00 ©2009 IEEE
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2) Lower initial investment and Lower expenses in
power electronics
3) Simple installation, maintenance and repair
4) Avoiding uncertain surveys for future of the system
5) Higher reliability.
The contribution of this paper is to propose a simple model
for a DSSC in Newton power flow. The model is obtained by
developing the SSSC model through desired objectives in
DSSC.
The structure of this paper is as follows. In section II, The
modeling principals are stated. The implementation of such
model in Newton power flow algorithm is covered in section
III. Simulation results in section IV demonstrates the
performance of the model and conclusion is given in section V.
II. DSSC MODELING
Figure 4. Three phase compensation [8].
Like a SSSC, a DSSC unit is represented as an independent
voltage source in series with transformer impedance. Fig. 5
shows such an equivalent circuit obtained for each phase
similarly and independently [8].
A. Operation Principles of DSSC
A DSSC unit, which is in series-connected with the
transmission line through the coaxial transformer, injects an
independent leading or lagging voltage with respect to the line
current in order to control the power flow of the line. In this
regard, a single DSSC unit behaves like a SSSC. Fig. 3 [7]
shows SSSC operation principals. Assume that a compensating
unit is attached to bus j and controls the power flow of line j-i.
This figure is also identical for a DSSC unit operation and is
valid for DSSC modeling.
Figure 5. Single phase equivalent circuit [8].
According to Fig. 5 if Vsep = Vsep ∠θ sep , Vip = Vi p ∠θ ip and
Vjp = V jp ∠θ jp then the power flow constraints of a DSSC unit
are:
Pijp = Vi
g iipp − Vi pV jp ( g ijpp cos(θ i p − θ jp ) + bijpp sin(θ i p − θ jp ))
p2
− Vi pV sep ( g ijpp cos(θ i p − θ sep ) + bijpp sin(θ i p − θ sep ))
Q = −Vi
p
ij
p2
pp
ii
b
− Vi V j ( g
p
p
pp
ij
sin(θ i − θ ) − b
p
p
j
pp
ij
(1)
cos(θ i − θ ))
p
p
j
− Vi pV sep ( g ijpp sin(θ i p − θ sep ) − bijpp cos(θ i p − θ sep ))
Figure 3. SSSC operation principals [7].
B. Equivalent Circuit and Power Flow Constraints
DSSC modeling is based on SSSC modeling with two
major differences. First, the DSSC units are placed
independently on system phases needing a three-phase model
and three-phase power flow as depicted in Fig. 4 [8]. The
second difference is the existence of several modules in a
DSSC system distributed uniformly along the line. Considering
all of these modules in the model is not practical, therefore, it is
assumed that the compensating system consist of three major
modules each containing more than one unit. These three
modules (per line, per phase) are installed at the beginning,
middle and the end of the transmission line.
Pjip = V j
p2
g jjpp − Vi pV jp ( g ijpp cos(θ jp − θ i p ) + bijpp sin(θ jp − θ i p ))
+ V jpVsep ( g ijpp cos(θ jp − θ sep ) + bijpp sin(θ jp − θ sep ))
Q jip = −V j
(2)
p2
(3)
biipp − Vi pV jp ( g ijpp sin(θ jp − θ i p ) − bijpp cos(θ jp − θ i p ))
+ V jpVsep ( g ijpp sin(θ jp − θ sep ) − bijpp cos(θ jp − θ sep ))
Where g ijpp + jbijpp =
1
, g iipp = g jjpp = g ijpp , biipp = b jjpp = bijpp and
Z sepp
p (a, b or c) represents line three phases.
By inserting the DSSC unit into the system, two new power
constraints are needed to solve for the unit voltage magnitude
and phase angle. The first constraint is the DSSC unit zero
active power exchange and the second is the active power flow
constraint of the compensated line given by (5) and (6)
respectively [7].
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(4)
{
}
PE = Re V sep I jip * = 0
{
p
se
Re V I
p*
ji
}= −V
p
i
p
se
+ V j V (g
Pjip − Pji
cos(θ i − θ ) − b
pp
ij
cos(θ − θ ) + b
V (g
p
p , Spec
pp
ij
p
se
p
p
j
p
se
p
se
pp
ij
sin(θ i − θ ))
pp
ij
sin(θ jp − θ sep ))
p
and the related Jacobian matrix J is presented by (10) on the
next page.
p
se
(5)
=0
(6)
III. DSSC IMPLEMENTATION IN NEWTON POWER FLOW
Fig. 6 shows the schematic of a compensated phase of an
arbitrary line say j − j ' . The objective is to control the
transmitted power through this line. Assume that the DSSC
unit is attached to bus j , consider the new PQ bus i , and
Pi ,pload = Qip,load = 0 , where the line section ji consists of only the
DSSC unit.
IV. SIMULATION RESULTS
A. Active Power Flow Control by SSSC
The active power flow control in Newton load flow
algorithm is carried out on two test systems. The first
simulation is performed on the IEEE 30-bus system [9] in the
case of single line, balanced load and a single compensator
unit per compensated line. Five cases are studied in this part.
In each case a SSSC is added to the system on an arbitrary line
while leaving the previous compensators intact. Case 1 is the
base case without compensation. In cases 2, 3 and 4, the
compensators increase the active power flow of the
compensated lines. Case 5 is similar to case 4 except that the
last compensator is utilized to reverse the power flow direction
of the line 5-7. The numerical results of these cases are
summarized in Table I.
Figure 6. Installing a DSSC unit.
TABLE I. RESULTS FOR THE IEEE 30 BUS SYSTEM
According to Fig. 6, the new line i − j ' is the former line
j − j ' while the other parts of the network remain unchanged.
Extending this type of installation to three DSSC units on a
phase in equal distance from each other results in Fig. 7 in
which three modules are installed by adding four new buses
each similar to bus i in Fig. 6.
Figure 7. A compensated line.
Case
Comp.
Line
ǻP (MW, %)
SSSCs' injection
No.
of
iter.
Case
1
-
-
None
4
Case
2
12-15
+8, (47%)
Vse12-15 = 0.053 șse12-15 = 44.5°
6
Case
3
12-15
2-6
+8, (47%)
+20, (32%)
Vse12-15 = 0.055 șse12-15 = 44.3°
Vse2-6 = 0.1278 șse2-6 = 80.3°
6
Case
4
12-15
2-6
10-21
+8, (47%)
+20, (32%)
+4.4, (28%)
Vse12-15 = 0.0561 șse12-15 = 44.3°
șse2-6 = 80.3°
Vse2-6 = 0.1278
Vse10-21 = 0.0339 șse10-21 = 108°
6
Case
5
12-15
2-6
10-21
5-7
+8,(47%)
+20, (32%)
+4.4, (28%)
-34.2, (-240%)
Vse12-15 = 0.667 șse12-15 = -45.5°
Vse2-6 = 0.1834 șse2-6 = 67°
Vse10-21 = 0.0214 șse10-21 =84.3°
Vse5-7 = 0.2733 șse5-7 = 99.4°
7
The power mismatches should hold for all buses in Fig. 7,
therefore:
ΔPl =
p
Pglp
−
Pdlp
− Pl = 0
p
(7)
ΔQlp = Q glp − Qdlp − Qlp = 0
(8)
Where Pl p and Qlp are respectively the real and reactive
power leaving the bus l at phase p while Pglp and Q glp are the
powers entering the bus, and Pdlp and Qdlp are the load powers
leaving the bus l .
According to Fig.4, a three-phase Newton power flow
algorithm with simultaneous solutions of power flow
constraints given by (5)-(8) can be presented by (9).
J. ΔX = − Δ F ( X )
-
The corresponding voltages in Table I are in p.u.
In cases 2-4, the compensators act independently.
In case 5, the direction of power flow in line 5-7 is
forced to reverse. This enforcement affects all powers
and results in different injected voltages. In this regard
the current of Line 12-15 and consequently its
compensator is the most affected line and unit
respectively.
(9 )
Where the vectors ΔX and ΔF (X) are
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Authorized licensed use limited to: UNIVERSIDADE DO PORTO. Downloaded on May 06,2010 at 15:57:52 UTC from IEEE Xplore. Restrictions apply.
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a
a
a
a
a
a
a
a
a
a
»
« ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j
»
« a
c
c
b
b
a
c
b
a
c
b
a
c
b
a
c
b
a
»
« ∂ș se ∂ș se ∂ș se ∂Vse ∂Vse ∂Vse ∂ș i ∂ș i ∂ș i ∂Vi ∂Vi ∂Vi ∂ș j ∂ș j ∂ș j ∂Vj ∂Vj ∂Vj
»
« b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
»
« ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j
»
« ∂ș a ∂ș b ∂ș c ∂V a ∂V b ∂V c ∂ș a ∂ș b ∂ș c ∂V a ∂V b ∂V c ∂ș a ∂ș b ∂ș c ∂V a ∂V b ∂V c
j
j
j
j
j
j
i
se
se
se
se
se
i
i
i
i
i
»
« se
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
»
« ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j ∂Q j
»
« a
b
c
a
b
c
a
b
c
a
b
c
a
b
c
a
b
c
»¼
¬« ∂ș se ∂ș se ∂ș se ∂Vse ∂Vse ∂Vse ∂ș i ∂ș i ∂ș i ∂Vi ∂Vi ∂Vi ∂ș j ∂ș j ∂ș j ∂Vj ∂Vj ∂Vj
B. Three-Phase Active Power Control by DSSC
The load flow problem with DSSC active power control
carried out on a 5-bus test system. The system data is given in
[10]. Simulation is done for four cases containing two balanced
and two unbalanced systems. The compensation is performed
by installing three DSSC units on each phase of the lines 3-4
and 4-5 as in Fig.7.
(10)
Case 6 is the base case 5-bus balanced system.
Case 7 is the balanced compensated 5-bus system. The
calculated line powers in case 6 are increased to arbitrary
higher quantities making specified line powers in case 7.
Cases 8 and 9 are similar to cases 6 and 7 respectively
except that the three-phase system is unbalanced. The results
for cases 6-9 are summarized in Table II and Table III.
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TABLE II. RESULTS FOR 5 BUS BALANCED SYSTEM
Case
no.
Case
6
Line
3-4
4-5
3-4
Case
7
P
h
a
s
e
a
b
c
a
b
c
-
P
spec.
P
calc.
DSSCs' injection
I
t
e
r
.
-
0.1939
0.1939
0.1939
0.066
0.066
0.066
-
4
a
0.3
0.3000
V=[0.048, 0.0664, 0.0013]
ș=[56, 231, 241]°
b
0.3
0.3000
V=[0.048, 0.0661, 0.0021]
ș=[296, 111, 138]°
c
0.3
0.3000
V=[0.0485, 0.0671, 0.0024]
ș=[176, 351, 1]°
V. CONCLUSION
7
4-5
a
0.2
0.2000
V=[0.0552, 0.0624, 0.0204]
ș=[47, 216, 50]°
b
0.2
0.2000
V=[0.0554, 0.0628, 0.0205]
ș=[287, 96, 290]°
0.2000
V=[0.0555, 0.0623, 0.0206]
ș=[167, 336, 170]°
c
0.2
-
The corresponding injected voltages in Tables II and III
are in p.u.
The most considerable problem in this part is to find
proper initial values for the load flow. This problem
originates from the dependency of program convergence
on the system initializations, specially the
compensators. This means that finding the best initial
values becomes harder as the number of compensator
units increases.
A three-phase model for a DSSC based on SSSC model
suitable for power flow analysis is proposed in this paper. The
DSSC system is a three phase system requiring a three phase
power flow. The limitation in inserting all DSSC modules into
the system leads to use three DSSC units on each compensated
phase. The model implementation in Newton power flow
algorithm is explained in order to control the active power
flow. Numerical results carried out on the IEEE 30-bus and the
5-bus test system demonstrated the feasibility of the proposed
three-phase DSSC model. Since the Newton power flow is
basically dependent on initial values, a convergence problem
observed in simulations due to such initialization.
Considering the simplicity of the proposed procedures and
the simulation results, the proposed DSSC model seems
suitable for realizing the capabilities of DSSC in increasing the
power systems controllability.
VI. REFRENCES
TABLE III. RESULTS FOR 5 BUS UNBALANCED SYSTEM
Case
no.
Case
8
Line
3-4
4-5
3-4
Case
9
P
h
a
s
e
P
spec.
P
calc.
DSSCs' Injection
a
-
0.1402
-
b
c
a
b
c
-
0.2059
0.2403
0.0642
0.0317
0.1039
-
a
0.2
0.2000
V=[0.0354, 0.0488, 0.0017]
ș=[56, 230, 243]°
b
0.25
0.2500
V=[0.0403, 0.0514, 0.0054]
ș=[298, 113, 311]°
c
0.3
0.3000
V=[0.0417, 0.0554, 0.0054]
ș=[181, 357, 190]°
a
0.1
0.1000
V=[0.0401, 0.0443, 0.0165]
ș=[30, 198, 225]°
b
0.06
0.0600
V=[0.0264, 0.0296, 0.0148]
ș=[270, 74, 105]°
c
0.15
0.1500
V=[0.0430, 0.0450, 0.082]
ș=[169, 336, 354]°
4
7
4-5
N. Hingorani, “Flexible AC transmission,” IEEE Spectrum, v. 30, No. 4,
Apr. 1993, pp 40-45.
[2] C. Schauder, M. Gernhardt, E. Stacey, T. Lemak, L. Gyugyi, T. W.
Cease, and A. Edris, “Development of a _100 MVar static condenser for
voltage control of transmission systems,” IEEE Trans. Power Delivery,
vol. 10, pp. 1486–1493, July 1995.
[3] L. Gyugyi, C. D. Shauder, and K. K. Sen, “Static synchronous series
compensator: a solid-state approach to the series compensation of
transmission lines,” IEEE Trans. Power Delivery, vol. 12, pp. 406–413,
Jan.1997.
[4] L. Gyugyi, C. D. Shauder, S. L. Williams, T. R. Rietman, D. R.
Torgerson, and A. Edris, “The unified power flow controller: a new
approach to power transmission control,” IEEE Trans. Power Delivery,
vol. 10, pp.1085–1093, Apr. 1995.
[5] D. Divan, W. Brumsickle, R. Schneider, B. Kranz, R. Gascoigne, D.
Bradshaw, M. Ingram and I. Grant, ‘‘A distributed static series
compensator system for realizing active power flow control on existing
power lines’’, IEEE PSCE Conference Records,
[6] Horjeet Johal,Deepak Divan, "Design considerations for seriesconnected distributed FACTS converters,” IEEE Trans. Ind App., vol.
43, no. 6, pp.1609-1618,Nov/Dec 2007.
[7] Xiao-Ping Zhang,” Advanced modeling of the multicontrol functional
static synchronous series compensator (SSSC) in Newton power flow,”
IEEE Trans. Power Sys., vol. 18, no. 4, pp. 1410-1416,Nov 2003.
[8] X.-P. Zhang, C.-F. Xue and K.R. Godfrey,” Modeling of the static
synchronous series compensator (SSSC) in three-phase Newton power
Flow,” IEE Proc.-Gener. Transm. Distrib., Vol. 151, No. 4, July 2004.
[9] Saadat ,Hadi(1999),”Power system analysis”, McGraw-Hill.
[10] Enrique Acha, Claudio R. Fuerte-Esquivel, Hugo Ambriz-Perez, Ce´sar
Angeles-Camacho, "(2004),"FACTS ,modeling and simulation in power
networks, John Wiley & Sons Ltd,.
[1]
I
t
e
r
.
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