International Journal of Engineering Trends and Technology (IJETT) – Volume 33 Number 3- March 2016
Analysis of Power System in the Presence of
Shunt and Series Facts Devices
M. Lakshmikantha Reddy#1, M. Ramprasad Reddy*2, Dr. V.C.Veera Reddy#3
#
Associate Professor, Department of EEE, Yits, Tirupati,
Associate Professor, Department of EEE, Ace, Madanapalli,
#
Former Professor & HOD, Department of EEE, S V University, Tirupati,
#
Abstract— To increase the transmission capacity in a
given system to meet the load raises the importance
of FACTS controllers. As these controllers not only
increases the transmission capacity but also
controlling the power flow through the predefined
transmission corridors. The effectiveness of modeling
and convergence is tested for any FACTS devices and
further it is analyzed with different FACTS
controllers like TCSC, SVC, STATCOM and UPFC.
The standard Newton-Rap son method is used to
solve the nonlinear power flow equations. The active
and reactive power flow control in AC transmission
networks was exercised by carefully adjusting
transmission line impedances, as well as regulating
terminal voltages by generator excitation control and
by transformer tap changes. Series and shunt devices
were employed to effectively change line impedances.
With inclusion of TCSC the real power flow is
improved and SVC, STATCOM results in improved
voltage profile where as UPFC increases real and
reactive power flow. These device models are tested
on IEEE-14 bus system and results are presented.
Keywords—SVC, TCSC, STATCOM, UPFC.
I.INTRODUCTION
Modern control centers of electrical power
systems are equipped with computational tools to help
time, with the increase in power demand, operation
and planning of large interconnected power system are
becoming more and more complex, and so power
system will become less secure. As the same
instability is one of the phenomena which results into
a major blackout. Planning the operation power
systems under existing conditions, its improvement
and also its future expansion require the load flow
studies. This is the most favored power flow method
and also based on the difference between power flow
in the sending and receiving ends, the losses in a
particular line can also computed. One of the main
strength of the Newton Raphson is its reliability
towards convergence.
The main aim of this paper is to model FACTS
devices in power flow study, and to obtain complete
voltage magnitude and phase angle information for
each bus in a power system for a specified load and
generator conditions. Once this information is known,
real and reactive power flow on each branch as well
as generator reactive power output can be determined.
ISSN: 2231-5381
Due to the nonlinear nature of this problem,
numerical iterative methods are employed to obtain
acceptable solution.
II. FACTS Devices
FACTS technology is concerned with the ability
to control, in an adaptive fashion, the path of the
power flows throughout the network, where before
the advent of FACTS, high-speed control was very
restricted. In this context, power flow computer
programs with FACTS controller modeling capability
have been very useful tools for system planners and
system operators to evaluate the technical and
economical benefits of a wide range alternative
solution offered by the FACTS technology [1]. The
FACTS devices are a high-end power technology
providing more flexibility, fast, reliable and efficient
operation of power system [2]. The FACTS
controllers can be broadly classified as:
A. Shunt Controllers
Shunt compensation is mainly used for reactive
power and voltage control. The Static VAr
Compensator (SVC) generates or absorbs shunt
reactive power at its point of connection. SVCs are
comprised of Thyristor Controller Reactor (TCR),
Thyristor Switched Capacitor (TSC), combined TCR
and TSC. Sample representation of the shunt
controller is shown in Fig.1.
Fig. 1. Representation of Shunt Controllers
B. Series Controllers
The principle of the series compensation is to
compensate the voltage drop in the line by inserting
the capacitive voltage or in other words to reduce the
effective reactance of the transmission line. The
FACTS based controllers to realize the series
compensation are Thyristor Controlled Series
Capacitor (TCSC) and Static Synchronous Series
Compensator (SSSC). But, SSSC is a gate-turn-off
(GTO) based voltage source converter FACTS
device. Sample representation of the series controller
is shown in Fig.2.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 33 Number 3- March 2016
Fig. 2. Representation of Series Controllers
C. Shunt-Series Controllers
The function of an SSSC (series compensator)
and a STATCOM (shunt compensator) can be
combined to form a new device known as Unified
Power Flow Controller (UPFC). The STATCOM and
SSSC share a common dc energy source, while acts
as an energy buffer. Thus UPFC offers a fast
controllable device for the flow of active and reactive
power in a line. Sample representation of the shuntseries controller is shown in Fig.3.
E. SVC Modeling
In practice the SVC can be seen as an adjustable
reactance with either firing angle limits or reactance
limits shown in Fig.5. The equivalent circuit is used
to derive the SVC non linear power equations and the
liberalized equations required by the N-R method [5,
6]. The current drawn by the SVC is and the reactive
power drawn by the SVC, which is also the reactive
power injected at bus-i is
Fig. 5. Equivalent circuit of SVC
Fig. 3. Representation of Shunt-Series Controllers
III. FACTS DEVICES MODELING
F. STATCOM Modeling
The STATCOM is represented by a synchronous
voltage source with minimum and maximum voltage
magnitude limits shown in Fig.6. The bus at which
STATCOM is connected is represented as a PQ bus,
which may change to a PQ bus in the events of limits
being violated.In such case, the generated or absorbed
reactive power would correspond to the violated
limit. The power flow equations for the STATCOM
are derived from the following voltage source
represented.
In this paper steady state model of FACTS
devices are developed for power flow Studies.
Considered FACTS devices are TCSC, SVC,
STATCOM, and UPFC [3, 4].
D. TCSC Modeling
The TCSC power flow model presented in this
section is based on the simple concept of a variable
series reactance, the value of which is adjusted
automatically to constrain the power flow across the
branch to a specified value, the amount of reactance
is determined efficiently using N-R method, the
changing reactance XTCSC represents the equivalent
reactance of all the series connected modules making
up the TCSC shown in Fig.4, when operating either
in inductive or in the capacitive regions.
Fig. 4. Equivalent circuit of TCSC
TCSC equivalent circuit inductive and capacitive
regions:
ISSN: 2231-5381
Fig. 6. Equivalent circuit of STATCOM
The source voltage equation:
G. UPFC Modeling
The UPFC equivalent circuit [7] consists of two
coordinated synchronous voltage sources for the
purpose of fundamental frequency steady state
analysis shown in Fig.7. the UPFC voltage sources are
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International Journal of Engineering Trends and Technology (IJETT) – Volume 33 Number 3- March 2016
Fig. 7. Equivalent circuit of UPFC
where,
and
are the controllable magnitude
and phase angle of the voltage source representing the
shunt converter and
and
are the controllable
magnitude and phase angle of the voltage source
representing the series converter. The magnitude of
the series injected voltage determines the amount of
power flow to be controlled.
The active and reactive power equations are:
Series converter:
Shunt converter:
IV. COMPUTATIONAL FLOW
NR method is the most popular technique used for
solving the resulting nonlinear system of equations.
This method begins with initial guesses of all
unknown variables. Taylor series is written with the
higher order terms neglected for each of the power
balance equations included in the system of equations
[8, 9].
NR approach is basically applied for nonlinear real
type system equations by liberalizing them around an
operating point with incremental changes. NR
method is not applicable for complex nonlinear
equations.
1. Read and print input data
2. Calculate the P injection and Q injection at all
buses.
3. Form Y-Bus using scarcity technique.
4. With voltage and angle (usually δ = 0) at slack bus
fixed, assume voltage magnitude and phase
angles at PQ buses and phase angles at all PV
buses. Generally flat voltage start will be used.
Set iter=0.
5. Set ΔP=0 and ΔQ=0.
6. Calculate the values of P and Q at all buses and
check for Q limits of PV buses. If there is a
ISSN: 2231-5381
violation in limits, change the bus status to load
bus for the current iteration and reinforce the
limits.
7. Compute ΔP for all buses except slack bus and ΔQ
for all PQ buses using corresponding equations. If
all the values are less than the prescribed
tolerance, stop the iterations, go to step 11.
8. If the convergence criterion is not satisfied,
evaluate elements of the Jacobian.
9. Solve the load flow equationusing Gauss
Elimination for correction vector.
10. Update voltage angles and magnitudes by adding
the corresponding changes to the previous values.
11. Increment iteration count (iter=iter+1). Check if
(iter<maximum iterations). If yes, return to step 5.
else, NR problem did not converge.
12. If the problem converges within the given
maximum number of iterations, print results and
stop.
V. RESULTS AND ANALYSIS
To verify the validity of the Newton Raphson
method, the IEEE-14 bus transmission system was
considered. The benefits obtained from the optimal
allocation of FACTS devices such as TCSC, SVC,
STATCOM and UPFC are increased power transfer
capability, improved voltage profile and reduced real
power losses.
In this paper the following four cases are analyzed:
Case-1: Only with one TCSC
Case-2: Only with one SVC
Case-3: only with one STATCOM
Case-4: only with one UPFC
IEEE 14 bus system with 5 generators and 20
transmission line has been considered to find the
efficacy of the proposed method without and with
FACTS devices. In 14 bus test system, bus 1 is slack
bus, while buses 2, 3, 6 and 8 are generator buses and
other buses are load buses.
As a preliminary computation, performance index
(PI) is calculated and then ranking is given for the
base case load flows without FACTS devices in
Table.1.
TABLE.I
PERFORMANCE INDEX RANKING ANALYSIS
Apparent
Line
Line
Bus
Power
limit
PI
Rank
No
code
Flow
(MV
(MVA)
A)
1
1-2
110.7099
150
0.5547
14
2
1-5
77.6511
85
0.8345
17
3
15-3
75.0012
85
0.7785
16
4
2-4
55.6050
85
0.4279
13
5
2-5
41.6491
85
0.2400
8
6
3-4
26.8299
85
0.0996
4
7
4-5
60.7671
150
0.1641
6
8
4-7
28.3196
30
0.8911
19
9
4-9
16.6770
32
0.2716
10
10
5-6
44.7379
45
0.9883
20
11
6-11
11.1060
14
0.6293
15
12
6-12
8.5526
32
0.0714
3
13
6-13
20.4126
22
0.8609
18
14
7-8
11.6057
32
0.1315
5
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International Journal of Engineering Trends and Technology (IJETT) – Volume 33 Number 3- March 2016
15
16
17
18
19
20
7-9
9-10
9-14
10-11
12-13
13-14
31.5911
5.1036
9.1753
7.1395
2.2168
7.5546
29
32
18
12
12
12
0.1866
0.0254
0.2598
0.3539
0.0341
0.3963
7
1
9
11
2
12
case-1
As the TCSC is a series controlled FACTS device a
line in which least power will flow is required for the
best location of TCSC. The required best location for
the TCSC is determined from base case results by
using performance index method. The PI values for
the test system are given in Table.1. From this table,
it can be seen that the line 9-10 is the best location for
the TCSC as it has least performance index. The line
flows and bus voltages of test system using proposed
method without and with TCSC are tabulated in
Table.2 and Table.3 respectively. From these tables,
it can be observed that the load flows, bus voltages
are improved by installing the thyristor controlled
series capacitors. Comparison of load flows and bus
voltages with and without TCSC is shown in Figs 8
and 9. From the Table.10, observations reveal that the
net loss is reduced from 5.0622MW to 4.5480MW by
installing TCSC device.
Line
No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
TABLE.II
VOLTAGE PROFILE
Without TCSC
With TCSC
Voltage
Voltage
Voltage
Voltage
Magnitude
Angle
Magnitude
Angle
(p.u)
(deg.)
(p.u)
(deg.)
1.0600
0
1.0600
0
1.0097
-4.5310
1.0165
-5.6270
1.0000
-13.1116
1.0000
-20.1035
0.9879
-10.2493
0.9949
-12.2672
0.9960
-8.7513
1.0032
-10.1810
1.0000
-15.2493
1.0000
-16.4996
0.9791
-13.7053
0.9832
-15.5111
1.0000
-13.7051
1.0000
-17.2973
0.9629
-15.5693
0.9556
-17.4834
0.9614
-15.8931
0.9739
-17.1372
0.9767
-15.6803
0.9835
-17.4851
0.9824
-16.2149
0.9778
-17.5689
0.9757
-16.2517
0.9808
-18.5797
0.9488
-17.0518
1.0044
-17.9674
Fig. 8. Voltage Magnitude variations without and with
TCSC
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TABLE.III
APPARENT POWER FLOW VARIATIONS
Line
no
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Bus
code
1-2
1-5
15-3
2-4
2-5
3-4
4-5
4-7
4-9
5-6
6-11
6-12
6-13
7-8
7-9
9-10
9-14
10-11
12-13
13-14
Without TCSC
(MVA)
110.7099
77.6511
75.0012
55.6050
41.6491
26.8299
60.7671
28.3196
16.6770
44.7379
11.1060
8.5526
20.4126
11.6057
31.5911
5.1036
9.1753
7.1395
2.2168
7.5546
With TCSC
(MVA)
125.4144
81.7415
74.5930
68.3740
66.8182
75.8560
88.9902
29..2762
18.2243
42.6957
12.3204
8.8674
20.7811
5.1225
28.8471
16.5417
12.4765
9.1935
13.9567
15.8559
Fig. 9. Apparent Power flow variations without &
with TCSC
1) Case-2
As the SVC is a shunt controlled FACTS device
the bus which suffers from low voltage profile is
required for the best location for the SVC. The
required best location for the SVC is determined from
base case voltage profile. From Table.4, it can be
seen that the bus 14 is the best location for the SVC
as it suffers from least voltage profile. The bus
voltages and line flows of test system using proposed
method without and with SVC are tabulated in
Tables.4 and 5 respectively.From these tables, it can
be observed that the load flows, bus voltages are
improved by installing the static VAr compensator.
Figs.10 and 11 shows the comparison of load flows
and bus voltages with and without SVC. Table.10
observations reveal that the net loss is reduced from
5.0622 MW to 4.9197 MW by installing SVC device.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 33 Number 3- March 2016
Li
ne
No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
TABLE.IV
VOLTAGE PROFILE
Without SVC
With SVC
Voltag
Voltage
e
Voltage
Voltage
Magnitu
Magnit
Angle
Angle
de
ude
(deg.)
(deg.)
(p.u)
(p.u)
1.0600
0
1.0600
0
1.0097
-4.5310
1.0000
-4.4063
1.0000
-13.1116
1.0000
-13.2251
0.9879
-10.2493
0.9865
-10.3413
0.9960
-8.7513
0.9972
-8.7912
1.0000
-15.2493
1.0000
-15.1516
0.9791
-13.7053
0.9858
-13.8603
1.0000
-13.7051
1.0000
-13.8603
0.9629
-15.5693
0.9781
-15.7265
0.9614
-15.8931
0.9787
-15.9528
0.9767
-15.6803
0.9831
-16.6994
0.9824
-16.2149
0.9886
-16.2062
0.9757
-16.2517
0.9873
-16.4731
0.9488
-17.0518
1.0000
18.1965
Fig. 11. Apparent Power flow variations without and with SVC
2) Case-3
As the STATCOM is a shunt controlled FACTS
device the bus which suffers from low voltage profile
is required for the best location for the STATCOM.
The required best location for the STATCOM is
determined from base case voltage profile. From
Table.6 it can be seen that the bus 14 is the best
location for the STATCOM as it suffers from least
voltage profile. The bus voltages and line flows of
test system using proposed method without and with
STATCOM are tabulated in Tables.6 and 7
respectively. From tables, it can be observed that the
load flows, bus voltages are improved by installing
the STATCOM. Figs.12 and 13, shows the
Comparison of load flows and bus voltages with and
without STATCOM. From the Table.10 observations
reveal that the net loss is reduced from 5.0622 MW to
4.9159 MW by installing STATCOM device.
Without STATCOM
Fig. 10. Voltage Magnitude variations without and
with SVC
Line
No
Voltage
Magnitude(
p.u)
TABLE.V
APPARENT POWER FLOW VARIATIONS
Line
Bus
Without SVC
With SVC
No
code
(MVA)
(MVA)
1
1-2
110.7099
117.0511
2
1-5
77.6511
78.2476
3
15-3
75.0012
75.9433
4
2-4
55.6050
56.1537
5
2-5
41.6491
42.1711
6
3-4
26.8299
32.1911
7
4-5
60.7671
81.9213
8
4-7
28.3196
28.5696
9
4-9
16.6770
16.9376
10
5-6
44.7379
40.7830
11
6-11
11.1060
13.7700
12
6-12
8.5526
22.9334
13
6-13
20.4126
17.8988
14
7-8
11.6057
24.9334
15
7-9
29.5911
27.4829
16
9-10
5.1036
6.1160
17
9-14
9.1753
9.6897
18
10-11
7.1395
9.7099
19
12-13
2.2168
6.5876
20
13-14
7.5546
14.2697
Total
652.3977
677.3578
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1.0600
1.0097
1.0000
0.9879
0.9960
1.0000
0.9791
1.0000
0.9629
0.9614
0.9767
0.9824
0.9757
0.9488
Voltage
Angle(deg.)
With STATCOM
Voltage
Magnitude
(p.u)
0
1.0600
-4.5310
1.0000
-13.1116
1.0000
-10.2493
0.9865
-8.7513
0.9937
-15.2493
1.0000
-13.7053
0.9858
-13.7051
1.0000
-15.5693
0.9781
-15.8931
0.9740
-15.6803
0.9831
-16.2149
0.9866
-16.2517
0.9873
-17.0518
1.0100
TABLE.VI
VOLTAGE PROFILE
Voltage
Angle(deg.)
0
-4.4063
-13.2251
-10.3413
-8.7912
-15.1561
-13.8603
-13.8603
-15.7265
-15.9528
-16.6994
-16.2062
-16.4731
-18.1965
Fig. 12. Voltage Magnitude variations without and
with STATCOM
ISSN: 2231-5381
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International Journal of Engineering Trends and Technology (IJETT) – Volume 33 Number 3- March 2016
TABLE.VII
APPARENT POWER FLOW VARIATIONS
With
Line
Bus
Without
STATCOM
No
code
STATCOM(MVA)
(MVA)
1
1-2
110.7099
121.1511
2
1-5
77.6511
82.2476
3
15-3
75.0012
64.5864
4
2-4
55.6050
58.1537
5
2-5
41.6491
42.2198
6
3-4
26.8299
15.1569
7
4-5
60.7671
62.9213
8
4-7
28.3196
25.5696
9
4-9
16.6770
21.9376
10
5-6
44.7379
42.6600
11
6-11
11.1060
9.7700
12
6-12
8.5526
16.5736
13
6-13
20.4126
20.8888
14
7-8
11.6057
7.9334
15
7-9
29.5911
29.4829
16
9-10
5.1036
17.1160
17
9-14
9.1753
21.6897
18
10-11
7.1395
8.7099
19
12-13
2.2168
9.5897
20
13-14
7.5546
12.9648
Total
652.3977
683.3228
Line
No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
TABLE.VIII
VOLTAGE PROFILE
Without UPFC
With UPFC
Voltage
Voltage
Voltage
Voltage
Magnitude
Angle
Magnitude
Angle
(p.u)
(deg.)
(p.u)
(deg.)
1.0600
0
1.0600
0
1.0097
-4.5310
1.0000
-4.2002
1.0000
-13.1116
1.0000
-26.2798
0.9879
-10.2493
0.9761
-14.2400
0.9960
-8.7513
0.9849
-11.5067
1.0000
-15.2493
1.0000
-18.3722
0.9791
-13.7053
0.9738
-17.5946
1.0000
-13.7051
1.0000
-17.5946
0.9629
-15.5693
0.9589
-19.2446
0.9614
-15.8931
0.9580
-19.4050
0.9767
-15.6803
0.9745
-19.0418
0.9824
-16.2149
0.9818
-19.3299
0.9757
-16.2517
0.9748
-19.3351
0.9488
-17.0518
1.0238
-19.8694
Fig. 14. Voltage Magnitude variations without and
with UPFC
Fig. 13. Apparent Power flow variations without and
with STATCOM
3) CASE 4
As the UPFC is a combined shunt-series
controlled FACTS device a line with least PI, which
is connected to a weak bus is required for the best
location of UPFC. The required best location for the
UPFC is determined from base case results by using
performance index method. The PI values for the test
system are given in Table.1. From this table it can be
seen that the line 13-14 is the best location for the
UPFC as it has least performance index and also
connected to a weak bus. The line flows and bus
voltages of test system using proposed method
without and with UPFC are tabulated in Tables.8 and
9 respectively. From these tables, it can be observed
that the load flows, bus voltages are improved by
installing the UPFC. Figs. 14 and 15, shows the
comparison of load flows and bus voltages with and
without UPFC. From the Table.10 observations
reveal that the net loss is reduced from 5.0622 MW to
4.1283 MW by installing UPFC device.
ISSN: 2231-5381
TABLE.IX
APPARENT POWER FLOW VARIATIONS
Line
Bus
Without UPFC
With UPFC
No
code
(MVA)
(MVA)
1
1-2
110.7099
127.0156
2
1-5
77.6511
81.2380
3
15-3
75.0012
37.7176
4
2-4
55.6050
94.2117
5
2-5
41.6491
69.8613
6
3-4
26.8299
21.6041
7
4-5
60.7671
78.0400
8
4-7
28.3196
26.6635
9
4-9
16.6770
23.6964
10
5-6
44.7379
42.8177
11
6-11
11.1060
12.7001
12
6-12
8.5526
28.8662
13
6-13
20.4126
20.6454
14
7-8
11.6057
14.4758
15
7-9
29.5911
27.4252
16
9-10
5.1036
18.0629
17
9-14
9.1753
11.2718
18
10-11
7.1395
8.4329
19
12-13
2.2168
11.3654
20
13-14
7.5546
15.0626
Total
652.3977
736.1575
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International Journal of Engineering Trends and Technology (IJETT) – Volume 33 Number 3- March 2016
[5]
[6]
[7]
[8]
[9]
Erinmez, LA., Ed., “Static Var Compensators”, Working
Group 38-01,Task Force No. 2 on SVC, CIGRE, 1986 .
GyugyiL.,“DynamicCompensationofACTransmissionLines
by Solid-stateSynchronous VoltageSources”, IEEE Trans.on
Power Delivery, Vol. 9, No.2,pp. 904-911,April 1994.
Gyugyi L., Schauder C.D., Williams S.L., Rietman
T.R.,Togerson D.R. and Edris A,: “The Unified Power Flow
Controller: A New Approach to Power Transmission
Control”,IEEE Trans. on Power Delivery, Vol. 10, No. 2, pp.
1085-1097, April 1995.
Maria G A., Yuen A.H. and Findlay J.A., “Control
VariableAdjustment in Load Flows”, IEEE Trans on Power
Systems, Vol.3 april 1988
Stott B., “Review of Load-flow Calculation Methods”, IEEE
Proceedings, vol. 62, pp. 916-929, July 1974.
Fig. 15. Apparent Power flow variations
without&with UPFC
Descri
ption
Device
location
Size in
(MVAr)
Loss(Mw
)
TABLE.X
SUMMARY OF TEST RESULTS
Withou
TCS
STATCO
t
SVC
C
M
FACTS
5.0622
9-10
14
14
0.025
6
4.548
0
11.01
5
17.0062
4.919
4.9159
UPF
C
13-14
0.108
0
4.128
3
VI. CONCLUSION
In this paper, the optimal placement of FACTS
devices based on Newton Raphson method by using
performance index method has been proposed for
improvement of voltage profile and to increase the
power transfer capability. By using the proposed
method, individual bus voltages and line flows and
net real power loss can be determined.In this paper,
four cases were considered. From these four cases it
can be observed that by installing any one of the
FACTS device such as TCSC, SVC, STATCOM, and
UPFC over loaded line flows and violation of bus
voltages can be maintained within the limits. It can
also be observed that these line flows and bus
voltages are improved by installing these FACTS
devices in appropriate locations. Finally, from all the
above four cases it can be concluded allocation of
UPFC is more effective in order to reduces real
power losses. For the validation of results the
standard IEEE- 14 bus test systemis considered.
REFERENCES
[1]
[2]
[3]
[4]
Hingorani N.G.,“HighPower Electronics and flexible AC
TransmissionSystems”IEEE Power EngineeringReview,pp.34, July1988.
Hingorani N.H.,“Flexible AC TransmissionSystems”,
IEEESpectrum, pp,40-45, April 1993.
Enrique Acha, Claudio R. Fuerte-Esquivel, Hugo AmbrizPérez, César Angeles-Camacho., “FACTS: Modeling and
Simulation of Power Networks”, Wiley, 2004, ISBN: 0-47085271-2.
AchaE.,
“AQuasi-NewtonAlgorithmfortheLoad
FlowSolutionofLarge
NetworkswithFACTSControlledBranches”,
Proceedings
ofthe28thUPEC
Conference,StaffordUK,pp.153-156,21-23September 1993.
ISSN: 2231-5381
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