International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013)
Modeling and Analysis of SVC, TCSC, TCPAR in Power Flow
Studies
N. M. G. Kumar, P. Venkatesh, Dr. P. Sangamewara Raju
1
Research Scholar, 3Professor, Dept of EEE, Sri Venkateswara University, Tirupati, India,
2
Asst .Prof, Dept of EEE, Sree Vidyanikethan Engineering College, Tirupati, India
Abstract — The paper mainly deals about the application of
flexible AC transmission system (FACTS) to increase the
power transfer capabilities for new operating scenarios in the
bulk power systems. With the effect of FACTS technology
improves transmission capabilities to reduce the system losses,
and also improves the loadability of the power system. FACTs
technology allows a better utilization existing transmission
and generation reserve margins in the deregulated electricity
market for various stability margins. In this paper discusses
about the study state models of SVC (Static VAR
Compensator),
TCSC(Thyristor
Controlled
Series
Compensator) and TCPAR (Thyristor Controlled phase angle
regulator) is investigated for load flow environment to
enhance the power transfer limits. A proposed algorithm has
been tested on IEEE – 5 bus and 30 bus system in a specified
line under voltage stability limits and results are tabulated.
The proposed technique is simple and able technique to
improve the system operation under study state condition.
In most of the reported studies, attention has been
focused on the ability of these devices to improve the
power system security by damping system oscillations and
minimal attempts have been made to investigate the effect
of these devices on power system reliability. The
opportunities arise through the ability of FACTS
controllers to control the interrelated parameters that
governs the operation of transmission systems including
series impedance and shunt impedance, current, phase
angle and damping of oscillations at various frequencies
below the rated frequency. These constraints cannot be
overcome otherwise, while maintaining the required system
stability, by mechanical means without lowering the
useable transmission capacity. By providing added
flexibility, FACTS controller can enable a line to carry
power closer to its thermal rating. Mechanical switching
needs to be supplemented by rapid-response power
electronics. The facts technology can certainly be used to
overcome any to the stability limits, in which case the
ultimate limits would be thermal and dielectric. Static VAR
controllers control only one of three important parameters
(voltage, impedance, phase angle) determining the power
flow in the AC power system viz. the amplitude of voltage
at selected terminals of transmission line . It has long been
realized that an all solid-state or advanced, static VAR
compensator, which is true equivalent of ideal synchronous
condenser, is technically feasible with the use of Gate
Turn-Off (GTO) Thyristor. The UPFC is recently
introduced FACTS controller which has the capability to
control all the four transmission parameters. The UPFC not
only performs the functions of STATCOM, TCSC, and the
phase angle regulator but also provides additional
flexibility by combining some of the functions of these
controllers. Most of the world’s electric supply systems are
widely interconnected. This is done for economic reasons,
to reduce the cost of electricity and to improve its
reliability, it must however be kept in mind that these inter
connections are very complex and they emerged gradually
based upon the requirements of various power utilities.
Keywords— Static VAR compensator, Thyristor Controlled
Series Compensator (TCSC), Thyristor Controlled phase
angle regulator (TCPAR), Newton – Raphson method ,
power flow.
I. INTRODUCTION TO FACTS DEVICES
The ability to control power flow in an electric power
system without generation rescheduling or topology
changes can improve the power system performance using
controllable components, the line flows can be changed in
such a way that thermal limits are not exceed, losses are
minimized, stability margins are increased and contractual
requirements are fulfilled without violating the economic
generation dispatch. Flexible AC Transmission systems
(FACTS) technology is the ultimate tool for getting the
most out of existing equipment via faster control action and
new capabilities. The most striking feature is the ability to
directly control transmission line flows by structurally
changing parameters of the grid and to implement highgain type controllers based on fast switching. The
application of FACTS devices to power system security has
been an attractive ongoing area of research.
418
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013)
These interconnections apart from delivering the power
pool power plants and load centres in order to pool power
generation and reduce fuel cost. Thus they reduce the
overall number of generating sources, but as the saying
goes a coin has two sides, like wise as the power transfer
grows. The power system becomes increasingly complex to
operate and system can become less secure for riding
through major outages. It may lead to large power flows
with inadequate control, excessive reactive power, and
large dynamics wings between different parts of the
system.
Thus the full potential of a transmission connection
cannot be utilized. It is very difficult to control such
transmission of power in such systems. Most of the
controllers designed in the past were mechanical in nature.
But mechanical controllers have numerous intrinsic
problems. Many power electronics controllers have been
designed to supplement the potentially faulty mechanical
controllers. These power electronic controllers are all
grouped in a category called flexible AC transmission
controller or FACTS controllers. Facts technology opens
up new opportunities for controlling power and enhancing
the usable capacities of present, as well as new and
upgraded lines, the possibility that current through a line
can be controlled at a reasonable cost enables large
potential of increasing the capacity of existing lines with
large conductors. Also, the use of one of the FACTS
controllers to enables corresponding power flow through
such lines under normal and contingency conditions. These
opportunities arise through the ability of FACTS
controllers to control the interrelated parameters that
govern the operation of transmission system. ―Series
Impedance, Shunt Impedance, Current, Voltage, Phase
angle etc.,‖ are some of the interrelated parameters that are
controlled. These constrains cannot be overcome while
maintaining the system reliability by mechanical means
without lowering the usable transmission capacity. By
providing added flexibility FACTS controllers can enable a
line to carry power closer to it thermal rating. It must
however be emphasized that FACTS is an enabling
technology, and not a one to one substitute. The FACTS
technology is not a single high power controller but rather a
collection of controllers, which can be applied individually
or in co-ordination with others to control one or more of the
interrelated system parameters mentioned above. A Wellchosen FACTS controller can overcome specific
limitations of designated transmission line on a corridor.
But all FACTS controller represent applications of some
basic technology, their production can eventually take
advantage of technologies of scale. Just as the transistor is
the basic element for whole variety of microelectronic
chips and circuits, the thyristor or high power transistor is
the basic element for a variety of high power electronic
controllers. FACTS technology also lends itself to
extending transmission limits in a step-by-step manner with
an incrementing investment as and when required. A
planner could force a progressive scenario of mechanical
switching means and enabling FACTS controllers such that
the transmission lines will involve a combination of
mechanical and FACTS controller to achieve the objective
in an appropriate, stage investment scenario. It is also
worth nothing that in implementation of the FACTS
technology, we are dealing with base technology, proven
through HVDC and high power industrial drives.
Nevertheless, as power semiconductor devices continue to
improve, particularly the devices with turn off capability
cost of FACTS controller tend to decrease.
II. BASIC CONCEPTS AND PROBLEM FORMULATION
N-R METHOD:
The most widely used method for solving simultaneous
nonlinear algebraic equations is the Newton-Raphson
method (NR). Newton’s method is found to be more
efficient and practical. The number of iterations required to
obtain a solution is independent of the system size, but
more functional evaluations are required at every iteration.
Since in the power flow problem real power and voltage
magnitude are specified for the voltage-controlled buses,
the power flow equation is formulated in polar form. This
equation can be rewritten in admittance matrix as
n
I i   YijV j
….(1)
j 1
In the above equation, j includes bus i. expressing this
equation in polar form, we have
n
…. (2)
I i   | Yij || V j |  ij j
j 1
The complex power at bus i is
Pi  jQi  Vi * I i
Ii
in equation 3
Pi  jQ j | Vi |    i  | Yij ||| V j | ij   j
….(4)
Substituting form equation 2 for
n
j 1
419
.… (3)
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013)
Separating the real and imaginary parts,
n
Pi   | Vi | | V j || Yij | cos( ij   i   j )
j 1
….(5)
….(10)
B | Z |  ,
.… (11)
n
Qi   | Vi | | V j || Yij | sin( ij   i   j )
j 1
 J1
P 
Q    J


 3
J 2  



J 4   | V |

Z
) | A | 
2
X
  tan1 
R
A  (1  YCP *
  1   2
….(6)
…. (12)
If series compensation is provided, then:
  tan 1 

….(7)
By running the load flow analysis using NR-method we
can fine the Power flows in individual lines and loss

…. (13)
X  XC 

R

Now assume that power flow in a line is to be regulated
to a desired value (Pspecified) Psp, then the corresponding new
value of B i.e. Bnew can be found out using the equation
given below
III. MODELING OF FACTS DEVICES
(1) Static VAR compensator (SVC):
In this paper, Static VAR compensator is considered as
simple injecting the reactive power into the transmission
line.
Bnew 
| V1 || V2 | cos(   ) | A || V2 | cos(   ) … (14)
Pspecified
Note that Bnew is also given by the equation
1
Bnew  ( R 2  ( X  X C ) 2 ) 2 from
which Xc can be calculated.
Consider the initial line reactance X = Xline of
uncompensated. With the Xc in the line the resultant line
reactance is given by
X = X - Xc
.... (15)
The equation (14) is a highly nonlinear equation and
need to be solved iteratively and update X using eqn. (15)
accordingly. With the series compensation in the line
X  X C will be small compared to β of the
  tan 1 (
)
R
uncompensated line. Keeping this fact in mind, the X c
calculations can be made in three stages as mentioned
below.
Fig.1. Reactive power injected model of SVC
SVC can be used for both inductive and capacitive
compensation. In this project work the SVC is modelled as
an ideal reactive power injection at bus i.
i.e
Qi  QSVC
.… (8)
(2) Thyristor-controlled series compensator (TCSC)
Consider a transmission line with its ABCD parameters
as two port model shown below figure 2
A. Stage 1
Calculate β = tan-1 (Xline / Rline), from uncompensated
condition. Then considering incremental approach to avoid
the higher correction step, take
β1=50% of βold
.... (16)
Then solve equation (14) for finding Bnew using the
V11 and V2  2 of the desired line obtained from the
converged voltages of base case loads flows. The
corresponding Xc will be
X-Xc = (Bnew2 – R2)1/2
.… (17)
With this Xc in the line compensation reactance, the
resulting reactance is
X=X-Xc
.... (18)
Fig.2. Two port model of a Transmission line
The power at the receiving end P2 is given by
P2 
| V1 || V2 | cos(   ) | A || V2 | cos(   )
|B|
.…(9)
420
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Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013)
B. Stage 2
(3) Thyristor controlled Phase angle regulator (TCPAR)
Mathematical Modeling of TCPAR
In this approach the TCPAR is represented in power
injection model and it regulates the angle of the transformer
in intern to improve power flow and reduce the power
system loss. The static representation of TCPAR is shown
in Fig. 3. The Line Model with Thyristor Controlled Phase
Angle Regulator (TCPAR) has shown in below Fig. 4. The
real power flow (Pij) and reactive power flow (Qij) in a linek connected between bus - i and bus - j can be written,
without any TCPAR, as
With the above resulting X= (X-Xc) as the effective or
net reactance of the desired line, re-run the load flow
solution. Now new values of voltages of the line end
buses i.e. V1  1 and V2  2 are available. Re compute the
parameters A=| A |α and B=| B | β1, where β1 from
equation (16), and X given by equation (18) As the solution
of equation (13) is nearer to the final solution, β2 is to be
taken as
β2=80% of β1
……(19)
Once again solve equation (14) for finding Bnew using
latest values of V11 and V2  2 and update the value of
2
Pij  VV
i jYij cos(ij   i   j )  Vi Yij cos ij
Qij  Vi 2Yij sin ij  ViV j sin(ij   j   i ) 
X using equations (17) and (18).
…..(23)
2
Vi Ysh
2
….. (24)
C. Stage 3
With the above resulting X=(X- Xc) as the effective or
net reactance of the desired line, re-run the load flow
solution. Now new values of voltages of the line end buses
i.e. V1 1 and V2  2 are available. Recomputed the
parameters A=| A |α and B=| B | β2; where β2 from
equation (19), and X given by equation (18) as the solution
of equation (13) is nearer to the final solution, β3 is to be
taken as
β3 =100% of β2
…….(20)
Once again solve equation (13) for finding B new using
latest values of V1 1 and V2  2 and update the value of X
Fig: 3 Static Representation of TCPAR
using equations (17) and (18).Re-run the load flow and
compute the Xc and Xfinal. By the completion of the 3rd
stage calculations, the accurate value of Xc is available. At
every stage of the above approach calculate the power flow
(Pcal flow) of the line under consideration and its mismatch
between Psp and Pcal flow. Calculate the % error of the flow
in the line at the end of 3rd stage. This error indicates the
level of accuracy observed in the results produced by the
proposed algorithm.
Fig: 4. power injection model of TCPAR
Where, Vi and i are the voltage magnitude and angle at
bus i. Yij and ij are magnitude and angle of ith to jth element
of Y Bus matrix. Ysh is the full line charging admittance of
line. In a thyristor controlled phase angle regulator, the
phase shift is accomplished by adding or subtracting a
variable voltage component in perpendicular to the phase
voltage of the line. Fig.3 shows the static model of a
thyristor controlled phase angle regulator. The effect of
TCPAR can be modelled by a series inserted voltage source
VT and a tapped current IT. The additional voltage source
changes the bus voltage from Vi to Vj1 corresponding to the
shifting of the voltage by an angle α. The basic
relationships is
D. Alternate method using reactance compensation
The reactance of transmission line and is compensation
factor of TCSC is modeled by changing transmission line
reactance as below
Xnew =Xline + XTCSC
…… (21)
XTCSC= rTCSC * Xline
…… (22)
Where Xline is reactance of transmission line and is
compensation factor of TCSC is depended on transmission
line where it is located. To prevent overcompensation,
TCSC reactance is chosen between -70% of Xline to 20% of
Xline .
Vi1 e j

Vi
k
V  Vi (1  j tan  )
1
i
421
….. (25)
… (26)
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Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013)
VT  j tan 
… (27)
Where, k=cosα. is the transformation coefficient of the
voltage magnitude and α is the controllable parameter of
TCPAR. Neglecting losses in the TCPAR, the current
relationships can be written as
Vi I i*  Vi1 I i1
… (28)
 j
11
i
I
e

Ii
k
… (29)
I i  IT  I i1
… (30)
IT   jI tan 
… (31)
1
i
Fig 5. Test System: IEEE 5 bus system
The power flow equations from bus I to bus j can be
written as
S ij  Pij  jQij  Vi I ij*  Vi ( I T  I i* )*
… (32)
Based on this relationship, the real and reactive power
flow equations can be written as
P  tViViYij cos( ij   i   j )  t 2Vi 2Yij cos  ij … (33)
Q  t 2Vi 2Yij sin ij  tVV sin(ij   i   j ) 
t 2Vi 2Ysh
2
… (34)
Where t=1/ cosα
The injection model of TCPAR is shown in Fig: 4.The
injected active power at bus- i (Pis) and bus- j (Pjs) and
reactive power powers (Qis and Qjs) of a line having phase
shifter are
Pis  Vi 2T 2 g ij  ViV j T ( g ij sin  ij  bij cos  ij )
... (35)
Qis  Vi Tbij  VVT ( g ij cos  ij  bij sin  ij )
… (36)
Pjs  ViV j T ( g ij sin  ij  bij cos  ij )
... (37)
Q js  ViV j T ( g ij cos  ij  bij sin  ij )
… (38)
2
Fig 6. Test System: IEEE 30 bus system
V. RESULTS
(1) SVC (Static var compenciator)
The change in injected reactive power at 4 and 5 buses is
32MVAR
Where T=tan 
gij + jbij is the series admittance of the line connected
between bus - i and bus- j.Equations (33) and (34) have
been used to model TCPAR in congestion management.
Table: 1
Results before and after placement of SVC for IEEE 5 bus
System
IV. SYSTEM INVESTIGATED
Bus
No
In the paper IEEE 5 and 30 bus system test by using
proposed algorithm
1
2
3
4
5
422
Without FACTS
phase
Voltage
angle
pu
deg
1.060
0.000
SVC at bus 4
phase
Voltage
angle
pu
deg
1.060
0.000
SVC at bus 5
Voltage phase
angle
pu
deg
1.060
0.000
1.000
0.984
0.979
0.970
1.000
1.003
1.005
0.979
1.000
0.987
0.984
0.972
-2.245
-3.906
-3.971
-5.570
-2.055
-4.886
-5.285
-5.846
-2.061
-4.637
-4.957
-5.765
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013)
Table: 4(b)
line loss without and with SVC Devices for IEEE 30 bus system
Total system loss without SVC 6.122 MW,
10.777MVAR, Total system loss with SVC at 5 bus is
6.182 MW, -10.956 MVAR, Total system loss with svc at 4
bus 6.129MW,
-11.210 MVAR
Table: 2(a)
Power flows without and with SVC Devices for IEEE 5 bus
Location
2-4
3-4
4-5
2-5
4-5
27-30
29-30
power flows
Without SVC
With SVC
P MW
Q MVAR
P MW
Q MVAR
27.71
-1.72
27.80
-12.92
19.38
2.86
19.65
-12.29
6.59
0.51
6.87
6.05
54.66
5.55
54.95
-17.63
6.59
0.51
6.42
0.06
Total system loss without TCSC 6.122 MW,
10.777MVAR for IEEE-5 bus system. The total system
loss without TCSC is 17.599MW, 22.244MVAR for IEEE30 System
(2) TCSC (Beta compensation technique)
In IEEE 5 and 30 bus system, TCSC is placed in Line:
2-4
Table: 2(b)
line loss without and with SVC Devices for IEEE 5 bus system
Location
2-4
3-4
4-5
2-5
4-5
Table: 5(a).
Power flow and line loss without and with TCSC Devices for IEEE 5
bus system
Line losses
Without SVC
With SVC
P MW
Q MVAR
P MW
Q MVAR
0.46
-2.55
0.53
-2.41
0.04
-1.82
0.05
-1.86
0.04
-4.65
0.09
-4.63
1.21
-2.55
1.31
0.93
0.04
-4.65
0.06
-4.77
Beta
1
2
3
4
18
30
Beta
Compensation
(%)
0%
50%
80%
100%
SVC at bus 30
Voltage
Phase angle
pu
deg.
1.060
0.000
1.043
-5.496
1.022
-8.005
1.013
-9.662
1.029
-16.867
1.008
-18.222
Line losses
P
Q
MW
MVAR
0.50
-2.51
1.19
-2.65
1.18
-2.64
1.36
-2.77
Reactance
X=X-Xc
0.1703
0.1153
0.1132
0.0960
Power flows
P
Q
MW
MVAR
36.069
3.705
44.428
1.679
44.813
1.543
48.179
0.161
Line losses
P
Q
MW
MVAR
0.699
-1.812
1.041
-1.794
1.059
-1.797
1.219
-1.847
(4) TCPAR (Thyristor controlled Phase angle regulator)
For 5 bus system with r = 0.01; gamma=10; alpha=0.5
Table: 6.
TCPAR is placed in between the line 2 and 4 in IEEE 5 bus system
Table: 4(a)
Power flow without and with SVC Devices for IEEE 30 bus system
27-30
29-30
0.176
0.065
0.066
0.051
Power flows
P
Q
MW
MVAR
28.02
-8.96
40.22
-21.21
40.30
-21.03
42.16
-24.35
Table: 5(b).
Power flow and loss without and with TCSC Devices for IEEE 30 bus
system
The total system loss without SVC is 17.599MW,
22.244MVAR, the total system loss with SVC is 17.563MW,
22.055MVAR
Location
X=X-Xc
0%
50%
80%
100%
Table: 3
Results before and after placement of SVC Device for
IEEE 30 bus system
Bus
Reactance
Compensation
(%)
Similarly for 30 bus system the change in injected
reactive power at 30 buses is 2 MVAR
Without FACTS
Voltage Phase angle
pu
degree
1.060
0.000
1.043
-5.497
1.022
-8.004
1.013
-9.661
1.028
-16.884
0.995
-18.015
Line losses
Without SVC
With SVC
P MW
Q MVAR
P MW
Q MVAR
0.16
-0.30
0.15
-0.285
0.03
-0.06
0.03
-0.060
Location
Bus No
2
4
Power flows
Without SVC
With SVC
PMW
Q MVAR
P MW
Q MVAR
6.93
- 1.35
7.08
-0.46
3.67
-0.54
3.70
-0.21
Voltage pu
Before
After
1.000
1.000
0.984
0.988
Angle deg
Before
After
-2.061
-2.030
-4.957
-4.879
Before TCPAR device Total loss: 6.122MW, 10.777
MVAR, after TCPAR placed total loss: 6.050 MW,
-11.114 MVAR
423
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Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013)
Table: 7(a)
Power flow without and with TCPAR Devices
Location
2-4
Power Flows
Before TCPAR
P MW
Q MVAR
27.7
-1.72
Table: 10(a)
Power flow and line loss without and with TCSC Devices for IEEE
5 bus system
After TCPAR
P MW
Q MVAR
29.5
-1.25
Table: 7(b)
Line losses without and with TCPAR Devices for 5 bus system with r
= 0.01; gamma = 10; alpha = 0.5
Line losess
Before TCPAR
P MW
Q MVAR
0.46
-2.55
Location
2-4
After TCPAR
P MW
Q MVAR
0.52
-2.42
Table: 8.
TCPAR is placed at 2-4 in IEEE 30 bus system
Voltage pu
Before
After
1.043
1.043
1.013
1.015
Angle deg
Before
After
-5.497
-5.497
-9.661
-9.462
Table: 9(a)
Power flows without and with TCPAR for IEEE 30bus system with r
= 0.01,gamma = 20, alpha=.5
Location
2-4
Power Flows
Before TCPAR
P MW
Q MVAR
45.71
2.70
Location
2-4
0%
-70%
-50%
-10%
10
20
0.176
0.054
0.027
0.0243
0.02674
0.032076
Power flows
P
Q
MW
MVAR
28.02
-8.96
44.27
-12.35
49.38
-18.60
49.90
-19.38
49.43
-18.67
48.40
-17.21
Line Losses
P
Q
MW
MVAR
0.50
-2.51
1.24
-2.80
1.62
-3.16
1.67
-3.22
1.63
-3.17
1.54
-3.08
Reactance
Compensation
(%)
Reactance
(Xline)
0%
-70%
-50%
-10%
10
20
0.1703
0.0522
0.0261
0.0235
0.0258
0.0309
Power flows
P
Q
MW
MVAR
36.069
58.570
65.573
66.247
65.652
64.302
3.705
-6.946
-6.145
-7.416
-6.288
-14.000
Line Losses
P
Q
MW
MVAR
0.699
1.810
2.358
2.424
2.365
2.242
-1.812
-2.23
-2.80
-2.88
-2.81
-2.67
VI. CONCLUSIONS
A simple and efficient load flow technique has been
carried out for solving the IEEE 5 and IEEE 30 bus system.
It is evident that the concept has fast convergence
characteristics. It can be used for single line or multi lines
compensation
calculations
without
much
extra
computational burden. The work has been carried out by
placing the deferent types of FACTS devices is placed in
specified locations using in the test systems to minimize
the power losses, improve the voltage profile, reduction in
power losses and enhance the power transfer capabilities.
After TCPAR
P MW
Q MVAR
48.67
6.67
Table: 9(b)
Line losses without and with TCPAR for IEEE 30 bus system with r =
0.01,gamma = 20 ,alpha = 0.5
Line losess
Before TCPAR
P MW
Q MVAR
1.10
-0.51
Reactance
(Xline )
Table: 10(b)
Power flow and loss without and with TCSC for 30 bus system
Before TCPAR Total loss: 17.599 MW, 2.244MVAR
After TCPAR Total loss: 17.309 MW, 21.119MVAR
Bus
No
2
4
Reactance
Compensation
(%)
After TCPAR
P MW
Q MVAR
1.25
-0.10
REFERENCES
From the above results it is evident that power flows is
improved and loss is reduced in this technique.
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Devices XTCSC= rTCSC *Xline;
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Electronics Engineering from Bangalore University
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(PSOC) at S.V.U.college engineering, Tirupati.
Area of interest are power system planning, power system
optimizations, power system reliability studies, Real time
application of power system and like non-linear controllers
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University at S.V.P.C.E, T. Putter. and Obtained his
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425