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operators according to the fitness information obtained from
the environment, so that the individuals of the population
can
be expected to move towards better solution areas. The PSO
algorithm was first introduced by Eberhart and Kennedy [12],
[13]. Instead of using evolutionary operators to manipulate
the
individuals, like in other evolutionary computational
algorithms, each individual in PSO flies in the search space
with a velocity which is dynamically adjusted according to
its
own flying experience and its companions' flying
experience.Unlike in genetic algorithms, evolutionary programming,
and
evolution strategies, in PSO, the selection operation is not
performed. All particles in PSO are kept as members of the
population through the course of the run (a run is defined
as
the total number of generations of the evolutionary
algorithms
prior to termination). It is the velocity of the particle which
is
updated according to its own previous best position and the
previous best position of its companions. The particles fly
with the updated velocities. PSO is the only evolutionary
algorithm that does not implement survival of the fittest.
PSO
is now applied for solving electrical engineering related
problems [14].
Optimal location of different types of FACTS devices in
the power system has been attempted using different
techniques such as Genetic Algorithm (GA), hybrid Tabu
approach and simulated annealing (SA). The best location for
a set of phase shifters was found by genetic algorithm to
reduce the flows in heavily loaded lines resulting in an
increased loadability of the network and reduced cost of
production [15]. The best optimal location of FACTS devices
in order to reduce the production cost along with the
devices
cost using real power flow performance index was reported
[16].A hybrid tabu search and simulated annealing was
proposed to minimize the generator fuel cost in optimal
power
flow control with multi-type FACTS devices[17]. The best
location of UPFC to minimize the generation cost function
and
the investment cost on the UPFC device was found using
steady state injection model of UPFC , continuation power
flow technique and OPF technique[18]. By using multiple
UPFC, the real and reactive power are regulated in real time
by a centralized optimal control scheme using evolutionary
programming algorithm to provide best voltage profile and
minimum overall transmission losses [10]. Power flow
algorithm with the presence of TCSC and UPFC has been
formulated and solved [19]. A hybrid GA approach to solve
optimal power flow in a power system incorporating FACTS
devices has been reported.
In this paper, applying PSO technique, the optimal
location of FACTS devices to achieve maximum system
loadability with minimum cost of installation of FACTS
devices ,while satisfying the power system constraints, for
single type (TCSC or UPFC, or SVC) and multi type
(combination of TCSC, UPFC and SVC) devices were found.
TCSC has been modeled as a variable reactance inserted in
the
line and SVC is modeled as a reactive source added at both
ends of the line. UPFC is modeled as combination of a SVC at
a bus and a TCSC in the line connected to the same bus.
Finding the optimal location of FACTS devices has been
formulated as a single objective problem to minimize the
installation cost of FACTS devices and to maximize system
loadability and applying penalty for line flow and voltage
violation constraints. The variables for the optimization
for
each device are its location in the network, its setting and
the
installation cost, in the case of single type devices. In the
case
of multi type devices, the type of device used is also taken
asanother variable for optimization. Computer simulations were
done for IEEE 6 and 30 bus systems. Maximum system
loadability (MSL), the number of FACTS devices required to
attain the MSL and the installation cost of FACTS devices
are
found.
II.PROBLEM FORMULATION
A.Objective
Optimal placement of FACTS devices considering the cost
of installation of FACTS devices has been mathematically
formulated and is given by the following equation:
Min IC = CS1000+ PF || J 1|| (1)
Where
IC optimal cost of installation of FACTS devices;
C Cost of installation of FACTS devices in US$/KVAR;
PF penalty factor ,value ranges from 1030 to 1035;
S operating range of the FACTS devices in MVAR;
The cost of Installation of UPFC, TCSC and SVC are given
by (2), and is taken from [20].
(2)
=BUS
BUS
LINE
LINE VSOVLJ (3)
Where
OVL Line overload factor for a line;
VS Voltage stability index for a bus;
The cost is optimized with the following constraints:
>
=max
max
max
|);1|exp(
;1
pqpqpq
pq
pqpq
PPifP
P
PPif
OVL
(4)
=
otherwiseV
VifVS
b
b
|);1|exp(
1.19.0;1
(5)
Where
pqP Real power flow between buses p and q ;
38.1273051.00003.0
75.1537130.00015.0
22.1882691.00003.0
2
2
2
+=
+=
+=
SSC
SSC
SSC
SVC
TCSC
UPFC
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max
pqP Thermal limit for the line between buses p and q;
bV Voltage at bus b;
, Small positive constants both equal to 0.1;
B. FACTS devices constraints
i) -0.8 XL XTCSC 0.2 XL p.u. (6)
ii) -100MVAR QSVC 100 MVAR (7)
iii) (6) and (7) for UPFCWhere
XTCSC Reactance added to the line by placing TCSC;
XL Reactance of the line where TCSC is located;
QSVC Reactive power injected at the bus by placing SVC;
C. Power flow constraints
0),( =Vg (8)
Where
(9)
for each PQ bus t
for each PV bus m, not
including reference
tP Calculated real power for PQ bus t;
tQ Calculated reactive power for PQ bus t;
net
tP Specified real power for PQ bus t;
net
tQ Specified reactive power for PQ bus t;
V Voltage magnitude at different buses;
Voltage phase angle at different buses;
III.OVERVIEW OF PSO
The inherent rule adhered by the members of birds and
fishes in the swarm, enables them to move, synchronize,
without colliding, resulting in an amazing choreography was
the basic idea of PSO technique [12], [13]. PSO is similar
to
EC techniques in which, a population of potential solutions
to
the problem under consideration, is used to probe the search
space. The major difference between the EC techniques and
Swarm Intelligent (SI) techniques is that EC technique uses
genetic operators whereas SI techniques use the physical
movements of the individuals in the swarm. PSO is developed
through simulation of bird flocking in two-dimensional
space.
The position of each agent is represented in X-Y plane
withposition (Sx, Sy), Vx (velocity along X-axis), and Vy
(velocity
along Y-axis). Modification of the agent position is
realized
by the position and velocity information.
Bird flocking optimizes a certain objective function. Each
agent knows its best value so far, called 'Pbest', which
contains the information on position and velocities. This
information is the analogy of personal experience of each
agent. Moreover, each agent knows the best value so far in
the
group, 'Gbest' among all Pbest. This information is the
analogy
of knowledge, how the other neighboring agents have
performed. Each agent tries to modify its position by
considering current positions (Sx, Sy), current velocities
(Vx,
Vy), the individual intelligence (Pbest), and the group
intelligence (Gbest).
The following equations are utilized, in computing the
position and velocities, in the X-Y plane:
vik+1 = W vi
k+ C1 rand1 (Pbesti - sik)
+ C2 rand2 (Gbest - sik
) (10)si
k+1 = sik+ vi
k+1 (11)
Where
vik+1 Velocity of ith individual at (k + 1 )th iteration;
vik Velocity of ith individual at kth iteration;
W Inertial weight;
C1,C2 Positive constants both equal to 2;
rand1 Random number selected between 0 and 1;
rand2 Random number selected between 0 and 1;
Pbesti Best position of the ith individual;
Gbest Best position among the individuals (group best);
sik Position of ith individual at kth iteration;
The velocity of each agent is modified according to
(10), and the position is modified according to (11). Theinertia
weight W is modified using (12), to enable quick
convergence.
iteriter
WWWW
=
max
minmaxmax
)((12)
Where
Wmax Initial value of inertia weight;
Wmin Final value of inertia weight;
iter Current iteration number;
itermax Maximum iteration number
The step by step algorithm for the proposed optimal
placement of FACTS devices is given below:
Algorithm:
Step 1. The number of devices to be placed, type ofFACTS device
to be used in the case of single type
of FACTS device and the initial load factor are
declared.
Step 2. In case of multi type of FACTS devices, typeof device is
also taken as a variable.
Step 3. The initial population of individuals is
createdsatisfying the FACTS devices constraints given by
(6) and (7) and also it is verified that only one device
is placed in each line.
Step 4. For each individual in the population, thefitness
function given by (1) is evaluated afterrunning load flow.
Step 5. The velocity is updated by (10) and newpopulation is
created by (11).
Step 6. If maximum iteration number is reached, thengo to next
step else go to step 4.
Step 7. If the final best individual obtained satisfiesthe
condition J=1, which means that the line flow
and bus voltage are within their maximum and
minimum limits, and then it is stored with its cost of
}
=
netmm
net
tt
net
tt
PVP
QVQ
PVP
Vg
),(
),(
),(
),(
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installation and settings. Increase the load factor and
go to step 3, else go to next step.
Step 8. Print the previous best individuals cost ofinstallation
and its settings.
Step 9. Stop.IV.RESULTS AND DISCUSSIONS
The solutions for optimal location of FACTS devices to
minimize the cost of installation of FACTS devices and
tomaximize system loadability for IEEE 6 and 30 bus systems
were obtained and discussed below. The simulation studies
were carried out on PentiumIV, 2.4 GHz system in
MATLAB 6.5 environment.
A. IEEE Six bus system
The bus data and line data of the six bus sample system are
taken from [21] and it contains 11 lines. The location,
settings
of FACTS devices and minimum installation cost are obtained
using the PSO technique for single type devices and it is
given
in Table I.
Fig. 1. System loadability curve for TCSC, SVC, UPFC and multi
type
device of 6 bus system
Fig. 2. Installation cost ($) Curve for placing various FACTS
devices of 6 bus
system
In addition, the effect of number of FACTS devices on
system loadability and the installation cost are also
observed
and are shown in Fig. 1 and Fig. 2 respectively. Ppqb, Qpqb
are
real and reactive power flow in the line p-q before placing
FACTS device and Ppqa, Qpqa are the real and reactive power
flow in the line p-q after placing FACTS device. In the case
of
TCSC, it is observed that placing TCSC in lines (1-2, 1-4,
1-5,
2-4, and 2-6) gives Maximum System Loadability (MSL) of
115% and the cost of installation is $ 0.368106. This is
indicated as point A in Figures 1 and 2. Among the 5 lines,
it
is observed that the improvement in power flow is high in
the
line 1-4 which is represented in bold case in Table I and
the
corresponding XTCSC setting is -0.029088 p.u. Similarly for
the
other cases, bold case in Table I represents the line in
which
maximum improvement in power flow occurs after placing
FACTS device. In the case of SVC, the MSL obtained is110% and
the minimum installation cost for SVC is $
9.73106and this is represented as point B in Fig. 1 and Fig.
2. The SVC has to be placed in lines (1-2, 1-4, and 2-4).
Placing SVC with QSVC setting of 96.571101 MVAR in line
(1-4) gives large improvement in power flow among the lines,
where SVC is placed. In the case of UPFC, to achieve MSL of
122%, UPFC have to be placed in lines (1-2, 1-4, 2-3, 2-4,
and
2-6) and the installation cost is $ 32.3106 and it is shown
as
point C in Fig. 1 and Fig. 2.
In the case of single type of devices, UPFC shows best
performance with MSL of 122%. Next to UPFC, TCSC gives
MSL of 115%. SVC gives lowest MSL, since in this system
line flow limits violation dominates and also due to the
factthat SVC is used mainly to improve voltage stability, it
cannot
improve the MSL very much. Comparing the cost, TCSC is
the best option. Even though UPFC shows good performance
in improving MSL, it is very much costlier than TCSC.
In the case of multi type devices, the values tabulated in
Table I are the best combination with minimum cost,
minimum number of devices required for attaining MSL and
their type. In this case, MSL of 116% is reached and placing
UPFC in line 2-5, it is observed that there is a large
improvement in power flow from the base case. The
installation cost for placing SVC in three lines, TCSC in
one
line, and UPFC in one line is $ 9.42106 and it is shown as
point D in Fig. 1 and Fig. 2. Placing UPFC in line 2-5
improves the power flow by about 100% of base case value
compared to other lines where FACTS devices are placed.
In all the cases shown, it is observed that FACTS devices
improve the line flows of the lines even to their thermal
limit.
It is concluded that for six bus system, TCSC is cost wise
cheaper while considering better improvement in system
loadability, but UPFC gives largest MSL. In all the cases
(single and multi type), one of the device is placed in line
1-2
and 1-4 and hence it is inferred that placing any type of
FACTS device in these lines will be beneficial in increasing
system loadability. From Fig. 1 it is observed that after
placing certain number of FACTS devices, both in single andmulti
type FACTS devices, the system loadability cannot be
improved further.
B. IEEE 30 bus system
The bus data and line data of 30 bus system are taken from
[11] and it contains 41 lines. The above said optimization
is
performed for this test data also. Fig. 3 shows the system
loadability with respect to the number of single and multi
type
of FACTS devices used.
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TABLE I
COMPARISON TABLE FOR LOAD FLOW IN LINES WHERE TCSC,SVC AND UPFC
ARE PLACED IN 6 BUS SYSTEM
MSLMAXIMUM SYSTEM LOADABILITY
Case Type of
Device
Used
From
Line
To
Line
Ppqb (MW) Qpqb(MVAR) Ppqa(MW) Qpqa(MVAR) Device setting
(p.u. for TCSC
, MVAR for
SVC)
Optimal
Installation
Cost in ($)
106
1 2 28.6897 -15.4187 39.7681 -21.1384 -0.009306
1 4 43.5849 20.1201 59.9769 19.3805 -0.029088
1 5 35.6009 11.2547 39.9259 10.8897 0.021361
2 4 33.0909 46.0541 28.9459 48.8949 -0.002585
TCSC
2 6 26.2489 12.3995 39.9239 13.2763 -0.073963
0.368
(MSL: 115%)
1 2 28.6897 -15.4187 33.5555 -17.4429 -79.50954
1 4 43.5849 20.1201 54.331 -3.8646 96.571101
SVC
2 4 33.0909 46.0541 29.967 2.3951 53.015082
9.73
(MSL: 110%)
1 2 28.6897 -15.4187 39.7034 -17.9088
1 4 43.5849 20.1201 59.5295 1.4559
2 3 2.9303 -12.2687 -10.0356 -8.5234
2 4 33.0909 46.0541 36.5896 42.9759
Single
type
UPFC
2 6 26.2489 12.3995 61.5946 36.6098
32.3
(MSL: 122%)
SVC 1 2 28.6897 -15.4187 39.5855 -21.0394 0.448685SVC 1 4
43.5849 20.1201 58.6958 10.0134 28.936442
TCSC 2 3 2.9303 -12.2687 4 -14.4129 0.043657
UPFC 2 5 15.5145 15.3532 28.9139 24.107
Multitype
SVC 3 6 43.7732 60.7242 48.1295 59.0285 5.993867
9.42
(MSL:
116%)
Fig. 3. System loadability curve for TCSC, SVC, UPFC and multi
type
devices of 30 bus system
Table II, shows the MSL, optimal cost of installation and
minimum number of devices needed for 30-bus system. The
MSL obtained for TCSC, SVC, UPFC and multi type of
devices are indicated as points A, B, C, and Drespectively in
Fig. 3 where the cost of installation is also
optimum. In all the cases, both in single and multi type of
FACTS devices, after placing 8 numbers of devices, the
system loadability is saturated and it does not increase
further.
Using single type of device, UPFC improves the system
loadability to 139%. TCSC gives MSL of 138%. SVC does
not improve the system loadability much, but it can be used
for very little loadability improvement. Comparing the cost
and system loadability, TCSC is the best option. Even though
UPFC improves the system loadability by a large amount, the
cost is high. So the correct option of these choices depends
on
the criterion, whether to minimize the cost or to maximize
system loadability.
TABLE II
INSTALLATION COST FOR MAXIMUM SYSTEM LOADABILITY WITH
MINIMUMNUMBER OF FACTS DEVICES OF 30 BUS SYSTEM
Type of
Device used
Maximum
System
loadability (%)
Minimum
number of
devices needed
Installation
cost in ($)106
TCSC 138 8 3.57
SVC 128 8 0.52
UPFC 139 8 276.7
Multi type 138 8 12.61
C. PSO parameters
The graphs showing the functional evaluation for different
values of population size (Np) and maximum number of
iterations (Ni) for 30 bus system using only TCSCs for MSL
of 138% are shown in Fig. 4. From the graphs, it is inferred
that selecting population size of 20 and maximum number of
iterations of 50 gives quick convergence and minimum
solution. When the population size and maximum number of
iterations are 30 and 75 respectively, it is observed that
best
minimum solution is obtained. Hence for 30-bus system
Np=30 and Ni=75 is chosen. It is observed that increasing Np
and Ni gives near global best solution. The values of both C
1,
C2 are taken as 2. The value of Wmax and Wmin are taken as
0.8
and 0.2 respectively.
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Fig.4. Functional evaluation graph for 30 bus system for TCSC
when system
loadability is 138%
V.CONCLUSION
This paper made an attempt to find the optimal location of
FACTS devices for getting maximum system loadability and
minimum cost of installation of FACTS devices, for single
type and multi type FACTS devices using PSO. Simulations
were performed on IEEE 6 and 30 bus systems. Optimizations
were performed on the parameters namely location of the
FACTS devices, their settings in the line, and the cost
ofinstallation for single type of devices. In the case of multi
type of FACTS devices, the type of device to be placed is
also
considered as a parameter in the optimization. In both
single
and multi type devices, it is observed that system
loadability
cannot be improved further after placing certain number of
devices. In IEEE test systems, UPFC gives maximum system
loadability but the cost of installation is high when
compared
with all other cases and TCSC requires minimum cost of
installation with better improvement in system loadability.
SVC gives lowest cost of installation in 30 bus system but
with minimum improvement in system loadability.
VI.ACKNOWLEDGEMENT
The authors express their sincere thanks to the
Management of Thiagarajar College of Engineering for
providing necessary facilities to carry out this research
work.
VII.REFERENCES
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management in restructured environment, pp. a71-a80, 2003.[8]
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[9] Stephane Gerbex, Rachid Cherkaoui, and Alain J. Germond,
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[10] T.T. Ma, Enhancement of Power Transmission systems by
usingmultiple UPFC on Evolutionary Programming, IEEE Bologna
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[11] P. Venkatesh, R. Gnanadass and Narayana Prasad Padhy,
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VIII.BIOGRAPHIES
M.Saravanan received his B.E. and M.E. degree in the year 1991
and 1992respectively. Presently he is working as Assistant
Professor of Electrical andElectronics Engineering at Thiagarajar
College Engineering, Madurai, India..He is currently pursuing PhD
degree at Madurai Kamarajar University,Madurai. His research
interests are FACTS and Power Electronics.
S.Mary Raja Slochanal received her B.E. ,M.E., and Ph.D. degree
in theyear 1981,1985 and 1997 respectively. She is currently
Professor of ElectricalEngineering at Thiagarajar College of
Engineering, Madurai, India. She has
published 36 research papers. Her fields of interests are power
systemmodelling, FACTS, reliability, unit commitment, and wind
energy.
P. Venkatesh received B.E. degree in electrical engineering ,
M.E. degreeand Ph.D. degree in the year 1991 ,1993 and 2003
respectively. He is
presently working as Assistant professor of Electrical and
ElectronicsEngineering at Thiagarajar College Engineering, Madurai,
India. His fields ofinterest are FACTS, Power system optimization,
Evolutionary Computationand Deregulation.
Prince Stephen Abraham. J received his B.E. degree in
electrical
engineering in the year 2003 and currently pursuing M.E. degree
at
Thiagarajar college of Engineering, India. His fields of
interest are FACTS
and Computer applications.
