Optimal Location of FACTS Devices for Congestion Management in Deregulated Power Systems
ABSTRACT In the emerging deregulated electric power market, congestion management becomes extremely important and it can impose barrier to electric power trading.,"There are two types of congestion management methodologies to relieve congestion in transmission lines. One is noncost free methods and another is costfree methods, among them later method relieves the congestion technically whereas the former is related more with the economics. In this paper congestion is relieved using cost free method. Among the various cost free methods, use of FACTS devices method is considered in this paper. The optimal location of TCSC and UPFC to relieve congestion in the network is proposed. In congestion management, the objective function is nonlinear hence for solving this function genetic algorithm (GA) technique is used. The above method is tested on IEEE 57bus system and it can be readily extended to any practical systems."

Conference Paper: Optimal power flow incorporating FACTS devices  bibliography and survey
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ABSTRACT: In the present day scenario private power producers are increasing rapidly to meet the increase demand due to heavily loaded customers. In this above process, the existing transmission lines are over loaded and lead to unstable system. Overloading may also due to transfer of cheap power from generator bus to load bus. New transmission lines or FACTS devices on the existing transmission system can eliminate transmission over loading, but FACTS devices are preferred in the modern power systems based on its overall performance For last two decades researchers developed new algorithms and models for power flow and optimal power flow incorporating FACTS devices so that cheap power can be made available to the customers without violating system stability. Still research is in progress to meet the present day congestion management problem with help of FACTS devices efficiently. The purpose of this survey is to collect information from the previous literatures and to support researchers in the above field to carry out further research. Therefore, the authors presented a complete bibliography and survey on the area of optimal power flow incorporating FACTS devices up to date.Transmission and Distribution Conference and Exposition, 2003 IEEE PES; 10/2003
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Optimal Location of FACTS Devices for Congestion
Management in Deregulated Power Systems
K.Vijayakumar
SRM University
Kattankulathur, Chennai
ABSTRACT
In the emerging deregulated electric power market, congestion
management becomes extremely important and it can
impose barrier to electric power trading.
t w o types of congestion management methodologies to
relieve congestion in transmission lines. One is noncost
free methods and another is costfree methods, among
them later method relieves the congestion technically
whereas the former is related more with the economics. In this
paper congestion is relieved using cost free method. Among
the various cost free methods, use of FACTS devices
method is considered in this paper. The optimal location of
TCSC and UPFC to relieve congestion in the network is
proposed. In congestion management, the objective function
is nonlinear hence for solving this function genetic algorithm
(GA) technique is used. The above method is tested on
IEEE 57bus system and it can be readily extended to any
practical systems.
General Terms
Congestion, Deregulated Power
Transmission Systems (FACTS), Thyristor
Series Capacitor (TCSC), Unified Power Flow
Controller (UPFC), Genetic Algorithms(GA), Optimal Power
Flow (OPF).
Keywords
FACTS, Unified Power Flow Controller (UPFC), Genetic
Algorithm (GA) Deregulation, Optimal Power Flow (OPF) .
1. INTRODUCTION
The restructuring in electric power sector has lead to larger use
of transmission grids. In deregulated power market, the
power system is operated almost to its rated capacity all
the times. Congestion may occur in transmission line
due to lack of coordination between generation and
transmission utilities. So congestion management becomes
very essential in deregulated power systems. In
regulated power system Transmission Companies
(TRANSCOs), Generation Companies
Distribution Companies (DISCOs) all come under
one organization, generally government. Whatever the
expenditure incurred on power system will be bared by the
government and at the same whatever revenue came it will go
to government. On the other hand in deregulated power systems
TRANSCOs, GENCOs, DISCOs
organizations [1][3]. To maintain the coordination between
them there will be one system operator in all types of
deregulated power system models, generally it is
Independent System Operator (ISO).
environment all the GENCOs and DISCOs make the
There are
System, Flexible AC
Controlled
(GENCOs) and
are under different
In deregulated
transactions ahead of time, but by the time of
implementations there may be congestion in some of the
transmission lines . Hence ISO has to relieve that congestion
so that the system is maintained in secure state. To relieve
the congestion ISO can use mainly two types of techniques
which are as follows [4][6]:
A.Costfree means
(i) Outaging of congested lines.
(ii) Operation of transformer taps/phase shifters.
(iii) Operation of FACTS devices particularly series devices.
B. Noncostfree means:
(i) Redispatch of generation in a manner different from
the natural settling point of the market. Some generators
back down while others increase their output. The effect
of this is that generators no longer operate at equal
incremental costs.
(ii) Curtailment of loads and the exercise of (notcostfree)
load interruption options.
Among the above two main techniques costfree means have
the advantages like it is not going to affect economical
matters, so to relieve the congestion GENCOs and DISCOs
will not come into picture. In this paper, FACTS devices are
used to relieve the congestion because they posses many
advantages as compared with the other techniques [7][13].
In congestion management the objective function and
constraints are nonlinear and nonconvex. To solve such
equations classical techniques offer good results but with a
slow convergence ratio and not always giving the optimal
solution. Genetic algorithms are also being applied to a wide
range of optimization and learning problems in many
domains. Genetic algorithms lend themselves well to power
system optimization, and can offer significant advantages
in a solution methodology and optimization
performance.
The rest of the paper is organized as follows: Optimal Power
Flow (OPF) problem is formulated for relieving
congestion management in Section 2, Section 3 describes
genetic algorithm technique. In section4, Static modeling of
TCSC and UPFC is discussed. Section 5, describes about
optimal locations of TCSC and UPFC. In section 6, results
and discussions are presented and finally the paper is
concluded with section 7.
2. PROBLEM FORMULATION FOR
CONGESTION MANAGEMENT
The basic principle for the transmission congestion
management could be illustrated with the help of the
traditional spot pricing theory. In this framework, the
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30
central dispatcher optimally dispatches the generators
such that the social welfare is maximized while
satisfying the operation and security related constraints.
Specifically, the dispatcher solves the following optimization
problem to maximize the social welfare:
Where, PGi, QGi are the real and reactive power generation at
bus i. Pdi, Qdi are the real and reactive power demands at bus
i.
Vi, δi are voltage and angles at bus i.
Pgi,min, Pgi,max real power minimum and maximum
generation limits at bus i.
Qgi,min, Qgi,max reactive power minimum and maximum
generation limits at bus i.
Pdi,min, Pdi,max real power minimum and maximum demand
limits at bus i.
Qdi,min, Qdi,max reactive power minimum and maximum
demand limits at bus i.
In the objective function CGi (PGi) is cost function for
generating real power PGi at bus i, BDi (PDi) and is the
demand function. Tij is the bilateral transaction between
supplier at node i and consumer at node j.
By solving above optimization problem the generation schedule
is be obtained and with this schedule the line flows are found.
Then line flows are checked whether within the maximum
limits are not, if any of the line exceeds the thermal limit
is said to be congested and it has to be relieved. To
solve the above optimization problem classical techniques
suffers from the local optima and they need auxiliary
information about the objective function [14]. By heuristic
search method global optima can be found. Among the
heuristic search methods genetic algorithm (GA) is one of
the good techniques [15] and it is used in this paper.
3. GENETIC ALGORITHM
Genetic algorithms are one of the best ways to solve a complex
optimization problem. GAs are very general algorithm and
can work well in any search space. Genetic algorithm will be
able to produce a high quality solution. Genetic algorithms
use the principles of selection and evolution to produce
several solutions to a given problem. Genetic algorithms
tend to thrive in an environment in which there is a very large
set of candidate solutions and in which, the search space
is uneven and has many hills and valleys. True, genetic
algorithms will do well in any environment, but they will
be greatly outclassed by more situation specific algorithms
in the simpler search spaces. They are, however, one of the
most powerful methods with which to (relatively) quickly
create high quality solutions to a problem.
The most common type of genetic algorithm works like
this: a population is created with a group of
individuals created randomly. The individuals in the
population are then evaluated. The evaluation function is
provided by the programmer and gives the individuals a
score based on how well they perform at the given task. Two
individuals are then selected based on their fitness, the
higher the fitness, higher the chance of being selected.
These individuals then "reproduce" to create one or more
offspring, after which the offspring are mutated randomly.
This continues until a suitable solution has been found or
a certain number of generations have passed, depending on
the needs of the problem.
Each GA includes several major operations [6]: (i)selection,
(ii)crossover and (iii) mutation. The selection operator picks
up the best solutions from the population, thus pushing the
search towards optimum. The crossover operation combines
two members of the population and generates two
offspring. The mutation operator randomly generates a point,
thus exploring all regions of the search space
Parent selection is a simple procedure where by
two chromosomes are selected from the parent population
based on their fitness value. Solutions with high fitness
values have a high probability of controlling new offspring
to the next generation. The selection rule used in this paper
is a simple roulettewheel selection.
Crossover is an extremely important operator for the GA.
It is responsible for the structure recombination (information
exchange between mating chromosomes) and the convergence
speed of the GA and is usually applied with high probability
(0.6 0.9). The chromosomes of the two parents selected are
combined to form new chromosomes that inherit segments
or information stored in parent chromosomes. Until now,
many crossover schemes, such as single point, multipoint, or
uniform crossover have been proposed in the literature.
Single point crossover has been used in this paper.
Mutation is the operator responsible for the injection of
new information. With a small probability, random bits
of the offspring chromosomes flip from 0 to 1 and vice
versa and give new characteristics that do not exist in the
parent population. In this paper, the mutation operator is
applied with a relatively small probability (0.0010.005) to
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every bit of the chromosome. The FF evaluation and genetic
evolution take part in an iterative procedure, which ends
when a maximum number of generations are reached.
4. GENETIC ALGORITHM
If load flows are performed with the optimal schedule
obtained from OPF, few of the line flows may exceeds line
limits. ISO has to relieve such congestion in the lines to
maintain the system in secure state. FACTS technology is
improved day by day because their flexible control and
versatility. Some of the advantages of FACTS devices are
[18]:
• Greater control of power, so that it flows on
prescribed transmission routes.
• Secure loading of transmission lines to level nearer their
thermal limits.
• Greater ability of transfer between controlled areas.
• Prevention of cascading outages.
• Damping of power system oscillations.
Among the FACTS devices Thyristor Controlled Series
Capacitor (TCSC) and Unified Power Flow Controller (UPFC)
are versatile devices and in this paper they are used to
relieve the congestion [16][22].
4.1 Modelling of Transmission line
Fig. 1 shows a simple transmission line represented by
its lumped Π equivalent parameters connected between
busi and busj.
Figure 1 Model of transmission line.
Let complex voltages at busi and busj are V i ∟δ i and
V j ∟δ j respectively. The real and reactive power flow from
busi and bus j (Pij and Qij ) can be written as:
Similarly the real and reactive power flow from busj and
busi (Pji and Qji) can be written as
4.2 Modelling of TCSC
The effect of FACTS devices like TCSC on the network
can be seen as a controllable reactance inserted in
the related transmission line. The model of the network with
TCSC is shown in Fig. 2.
Figure 2 Modelling of transmission line with TCSC
During steady state the TCSC can be considered as a
static capacitor/reactor offering impedance jXTCSC . The
controllable reactance XTCSC is directly used as a control
variable to be implemented in the power flow equations.
The real power and reactive power flow equation of the
branch k flowing from bus i to j can be expressed as:
The change in the line flows due to series capacitance can
be represented as a line without series capacitance with
power injected at the receiving and sending ends of the line as
shown in Fig. 3. The real power injections at busi (Pic) and
busj (Pjc) can be expressed, by subtracting eqn. (8) from eqn.
(12) and vice versa.
Figure 3 Injection model of TCSC
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4.3 Modelling of UPFC
Unified Power Flow Controller (UPFC) was devised for real
time control and dynamic compensation of ac transmissions
system, providing multifunctional flexibility required to solve
many of the problems facing the power delivery industry.
From conceptual viewpoint, the UPFC is a generalized
synchronous voltage source, represented at the fundamental
frequency by voltage Vs1 with controllable magnitude
(0≤Vs1≤Vs1max) and angle (0≤φs1≤2π) in series with
the transmission line. As far as construction is concerned
a UPFC consists of shunt (exciting) and series (boosting)
transformer, which are connected by two voltagesourced
converters using GTO thyristors valves and a DC circuit.
Inverter2 is used to generate a voltage source at the
fundamental frequency with
(0≤Vs1≤Vs1max) and phase angle (0≤φs1≤2π), which is
added to the AC transmission line by the series connected
booster transformer. As the series transformer injects series
voltage in line, the control of active and reactive power is
possible by changing the magnitude and angle of inserted
voltage. The real power flows from shunt converter to series
converter via a DC link. As both inverters are capable of
handling reactive power independently shunt transformer can
also inject reactive power on the bus thus helps in maintaining
better voltage profile. In this way the inverter output voltage
injected in series with the line can be used for direct
voltage control, series compensation, phase shifting and
their combination and shunt current can be used to
maintain good voltage profile. The schematic diagram of
UPFC is shown in Fig.4
variable amplitude
Figure 4 UPFC schematic diagram
Figure 5 Vector diagram of UPFC
UPFC has three controllable parameters, namely the
magnitude and the angle of inserted voltage (Vs1, ϕs1) in
linek and the magnitude of the current (Iq).The vector
diagram of UPFC is shown in Fig. 5 and circuit diagram is
given in Fig. 6. Based on the principle of UPFC operation and
the circuit diagram, the basic mathematical relations can be
written as:
Figure 6 Circuit diagram of UPFC
The power injection at busi can be written as:
Where, Ish is the shunt current due to line charging.
Figure 7 Injection model of UPFC
The effect of UPFC can be represented as injected power with
the network as shown in Fig. 7. The injected complex powers
Sig (= Pig+jQig) at busi and Sjg (= Pjg+jQjg) at busj can be
written as,
Where, S o is the complex power injection when
there is no UPFC. From eqn. 8, the real and reactive power
injections at busi can be derived as
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Similarly the real and reactive powers injections at
busj and busg can be derived as
5. OPTIMAL LOCATION FOR TCSC &
UPFC
Even though FACTS devices offer many advantages,
their installation cost is very high. Hence ISO has to locate
them at optimal locations. This task can be accomplished by
considering many factors like cost, thermal limits of
transmission lines, reactive power compensation, reduction of
system losses, voltage limits and stability limits. As the aim of
this paper is to relieve the congestion here considering line
loading optimal locations are obtained [18][22].
5.1 Objectives of Optimization
The objective function is built in order to penalize
the configurations of FACTS leading to overloaded
transmission lines. Only the technical benefits of the
FACTS controllers, in terms of loadability, are taken
into account. Therefore, for configuration of FACTS
devices, the objective function to maximize is given by,
(24)
Figure 8 Objective function vs line overload.
While the branch loading is less than 100%, its value is equal
to 1; then it decreases exponentially with the overload. To
accelerate the convergence, the product of all objective
function is taken. Equation (24) is solved using GA with the
initial population for a given power system of Nb
branches, is generated from the following parameters:
• NF the number of FACTS devices to be located optimally.
• the different types of devices to be located.
• Nv the number of possible discrete setting for a device.
• Ni the number of individuals of the population.
The creation of an individual is done in three stages. First, a
set of NF branches of the network are randomly drawn and is
put in the first string. The order of the branches is not
important and different individuals may represent the same
configuration of FACTS devices. After drawing the
branches where the FACTS devices will be located, the
next two steps consist in the attribution of the
characteristics of the devices. The second string, referred to
the types of the devices, is obtained by randomly drawing
numbers among the selected devices. Thus, if we decide to
optimally locate only one type of device, this string will
contain the same character. Setting values of the devices
are finally randomly drawn among the possible. To obtain
the entire initial population, these operations are repeated Ni
times.
Then, the objective function (Eqn (24)) is computed for
every individuals of the population. It represents a
mathematical translation of the optimization to realize and
does not have to be continuous or derivable. It has to be
elaborated so as to favor the reproduction of good individuals
without preventing reproduction of interesting other. In our
case, the objective function is defined in order to quantify the
impact of the FACTS devices on the state of the power
system. The move to a new generation is done from the
results obtained for the old generation. A biased roulette wheel
is created from the obtained values of the objective function of
the current population as represented in Fig. 9.
After that, the operators of reproduction, crossover and
mutation are applied successively to generate the offspring.
In turn, two individuals are randomly drawn from the
population and reproduced. The probability of drawing
an individual is proportional to its part on the biased
roulette wheel. Fig. 9(a) shows the process of reproduction.
The crossover may occur with a probability; generally close
to 1. A singlepoint crossover is applied as shown in Fig.
10. From the position of crossover point, elements of the three
strings of both parents are exchanged.
Mutations are possible independently on all elements of the
three strings of an individual. A specific probability is applied
for each string: for the first string, for the second and for
the last. These probabilities change with the generations.
When a mutation occurs on the first string, the one related
to the location, a new line among the set of branches
having no FACTS is randomly drawn. In the case of
mutation on the two other strings, a new value is drawn
among the set of possible ones. Examples of mutations are
shown in Fig. 11
Operations of selection, crossover and mutation are repeated
until the number of desired offsprings is created. The objective
function is then calculated for every offsprings and the best
individuals among the entire pool, comprising parents and
their offsprings, are kept to constitute the new generation..
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Inelastic load
Elastic load
Without
Transaction
With
Transaction
Without
Transaction
With
Transaction
Total
generation
cost
Customer
benefit
11320
13470
6160
8908
5902
7309
3663
4895
Social welfare
5417
6162
2497
4013
Total
generation
428.8
528.8
263.3
352.9
Total load
428.8
5288
263.2
352.9
Figure 9 Reproduction (a) Draws on the roulette wheel
(b) Selected individuals.
Figure 10 Cross over (a) Cross over point (b) After
crossover.
Figure 11 Mutation (a) Mutation point (b) After mutation.
In this way, the objective function of the best individual of
the new generation will be the same or higher than the
objective function of the best individual of the previous
generation. Similarly, the average fitness of the population will
be the same or higher than the average fitness of the
previous generation. Thus the fitness of the entire
population and the fitness of the best individual are
increasing for each generation. The termination criteria for
GA will be any one of the following two conditions:
(1). The maximum number of generations is achieved.
(2). When the genotype of the population of
individuals converges, the convergences of the genotype
structure occur when all bit positions in all string are
identical. In this case, crossover will have no further effect.
6. RESULTS AND DISCUSSIONS
The proposed model has been implemented on IEEE57
bus system. The social welfare given in equation (1) is
taken as Objective function for congestion management.
This objective function is solved using Genetic Algorithm.
The parameters used for GA is given in Table 1.
Table 1. Genetic Algorithm Parameters
Population size 150
0.01 Mutation rate
100% Crossover rate
Single point Crossover operator
Roulette wheel Selection operator
50 Maximum iterations
The optimal generation schedule for maximizing social
welfare with and without transaction for fixed load is given in
Table 2. A bilateral transaction of 100MW is considered
between supplier at node 5 and consumer at node 15. The
generation cost, customer benefit and social welfare for elastic
and inelastic loads are given in the Table 3.
Table 2. Optimal Generation schedule
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Table 3 Optimal social welfare
Without transaction
The fig. 12 shows the convergence criteria of the
objective function in maximizing the social welfare
without transaction. The line loading without transaction is
given in the fig. 13
With Transaction
The figure 14 shows the convergence criteria of the
objective function is maximizing the social welfare for
without transaction. The line loading without Transaction are
given in the fig.16. It is found that the line number 8
(connected between buses 5 and 6) is congested for a bilateral
Transaction of 100MW. The line thermal limit is taken 1.5pu
Figure 12 Social welfare vs iterations without transaction
Figure 13 Line loading without transaction
Figure 14 Social welfare vs iterations with transaction
.
Figure 15 Line loading without transaction
Generator No
1
2
3
4
5
6
7
Inelastic load
Elastic load
Without
0
0
19.1
0
277.1
0
132.7
Transaction
With
0
0
34.82
0
378.4
0
115.5
Transaction
Without
0
0
13.18
0
152.4
0
97.69
Transaction
With
0
0
13.88
0
246.7
0
95.18
Transaction
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Using FACTS Controller:
To relive congestion FACTS Controllers TCSC and UPFC
are considered. To find the optimal location of the
FACT controllers, the objective function Eqn 4.14. is
solved using Genetic Algorithm. The convergence of the
objective function is given fig.16 and fig.18
Two cases are considered
1. Locating Three TCSC
2. Locating Three UPFC
Case 1  Three TCSC
The optimal location of TCSC in the lines 15,16,19 are
obtained using Genetic Algorithm. It is found that while
using TCSC, the congestion in the line 8 is relieved from
1.9pu to 1.45pu. The line loading with three TCSC is shown in
fig. 17.
Figure 16 Ovl line vs. iterations with Three
TCSC Best: 0.8427
Figure 17 Line loading with TCSC
Case 2  Three UPFC
The optimal location of UPFC in the lines 15, 16, 19 are
obtained using Genetic Algorithm. It is found that by locating
UPFC, the congestion in the line 8 is relieved from 1.9 pu
to 1.37 pu. The line loading with three UPFC is shown in
figure 19. The Line loading reduction for locating three
UPFCs is more as compared with three TCSC.
Fig. 18 Ovl line Vs. iterations with three UPFC Best: 0.932
Figure 19 Line loading with UPFC
7. CONCLUSIONS
In this paper an algorithm for congestion management
using OPF has been proposed and it is solved using GA to
find the global optimal generation schedule for maximizing
the social welfare. By introducing a transaction i t i s
f o u n d t h a t the line loading was increased, i.e congested.
To relieve congestion multiple types of FACTS devices
are located optimally by considering thermal limits of the
lines.
Analysis is carried out by assuming two types of
FACTS devices. Line loading reduction in case of three
UPFCs is more as compared to three TCSCs. Above
method is tested on IEEE57 bus system and it can be
readily extended to any practical network.
In future other FACTS devices can be used for
relieving congestion. Social welfare maximization and line
overloading problem are solved separately in this paper. Both
objectives can be solved simultaneously using any multi
objective optimization techniques.
8. ACKNOWLEDGMENTS
My thanks to the experts who have contributed
towards development of this paper.
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