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An Effective Method for Maximizing Social Welfare
in Electricity Market via Optimal TCSC Installation

Thanh Long Duong

Faculty of Electrical Engineering Technology
Industrial University of Ho Chi Minh City

Ho Chi Minh City, Vietnam
duongthanhlong@iuh.edu.vn

Thuan Thanh Nguyen

Faculty of Electrical Engineering Technology
Industrial University of Ho Chi Minh City

Ho Chi Minh City, Vietnam
nguyenthanhthuan@iuh.edu.vn

Ngoc Anh Nguyen

Faculty of Electrical Engineering Technology
Industrial University of Ho Chi Minh City

Ho Chi Minh City, Vietnam
nguyenngocanh@iuh.edu.vn

Le Anh Tu Nguyen

Faculty of Electrical Engineering Technology
Industrial University of Ho Chi Minh City

Ho Chi Minh City, Vietnam
lenguyenanhtu@iuh.edu.vn

Abstract—The evolving electricity market has increased power

demand and has brought many social benefits. Meanwhile, the

transmission systems are not developed to the same extent
because building new lines is difficult for environmental and

political reasons. Hence, the systems are driven close to their

limits resulting in congestions and critical situations endangering

the system’s security. Due to this, the study of enhancing the

transfer capability of existing power networks to satisfy the

increased power demand, maximum social welfare, and ensure its
secure operation has become one of the challenges the

Independent System Operator faces in the electricity market. In

order to solve this problem without building more transmission

lines, the installation of FACTS devices can be a better

alternative. Among FACTS devices, thyristor-controlled series

compensator (TCSC) is one that can redistribute power flow in

the network to improve the transfer capability of the existing
system effectively. However, it is very difficult to implement. This

paper presents the implementation of the Cuckoo Optimization

Algorithm (COA) to solve the OPF problem which is formulated

as a nonlinear optimization problem with equality and inequality

constraints in a power system for social welfare maximization via

the optimal installation of TCSC devices. As Cuckoo Search

Algorithm (CSA), the COA also starts with an initial population-
based metaheuristic optimization inspired by the nature of brood

parasitism of some cuckoo species. However, unlike CSA, COA

uses the cuckoo’s style for egg-laying to optimize the local search

instead of using Lévy flights. This model is tested in IEEE 14 and

IEEE 30 bus systems. Simulations results are compared with GA

and GWO and show that the COA is one useful method for
TCSC installation to maximize social welfare.

Keywords-cuckoo optimization algorithm; FACTS; TCSC; social

benefits; electricity market

I. INTRODUCTION

Due to the rapid technological progress, the consumption of
electric energy increases continuously. For the last three
decades, many electrical power utilities have been forced to

change their way of operation from monopolistic structure to
competitive market structure. In Vietnam, pilot steps of the
roadmap for the application of electricity market approved by
the Prime Minister, are being applied and the country moves
towards a competitive electricity market. The basic idea of
deregulation is to make supply and demand competitive so that
all participants, i.e. generator companies, distribution
companies, and the customers maximize their individual
welfare. The supply or cost bid provided by a generator
company is the minimum asking price that it would accept for
supplying a particular amount of power. Similarly, the demand
or benefit bid of a consumer is the maximum price that it would
pay for consuming a particular amount of power. The
Independent System Operator (ISO) is responsible for the
buying and selling of power between generator and distribution
companies to the customers based on supply and demand bids,
which are prepared in such a way as to maximize social
welfare. In order to solve this problem, transmission
improvement methods are applied to achieve minimum
generation costs, subject to system security constraints. In
contrast, social welfare maximizing is the objective of most
studies in deregulated power systems. Several studies have also
been performed on congestion management to maximize social
and individual welfare [1-2], as well as social welfare
maximization considering reactive power and congestion
management in the deregulated environment [3]. Distributed
generator locations for social welfare maximization are
presented in [4]. These studies focused on a method for
increasing social welfare under congestion probability in
transmission networks.

Recently, Flexible AC Transmission Systems (FACTS) [5]
have also been utilized to solve the congestion problem and
maximize social welfare. Many studies have been proposed for
the improvement of existing power networks via optimal
location of FACTS [6-19]. Interior point method was used for
system expansion with UPFC to maximize social welfare and

Corresponding author: Thanh Long Duong

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to manage congestion [20]. In [21], Mixed Integer Non-linear
programming was used for optimal location of FACTS to
maximize social welfare based on multiple time periods. But it
ignored the impact of FACTS on the reactive power flow. In
[22] FACTS device thyristor-controlled series compensator
(TCSC) is optimally located for congestion management
maximizing social welfare using genetic algorithm (GA) and
GWO algorithm. An efficient GA was proposed for optimal
size and location of TCSC in a deregulated market for
congestion management with aim of maximizing the social
welfare cost [23]. In [24], a new fuzzy-based genetic algorithm
(Fuzzy-GA) for alleviating congestion and maximizing social
benefit in a double-sided auction market by locating and sizing
of one TCSC unit. In [25], a GA for finding the optimal
location and size of this device was proposed for congestion
management with the aim of increasing social welfare. A novel
efficient differential evolution and evolutionary programming
technique for social welfare maximization by optimal location
of various FACTS devices in pool electricity market based on
contingency analysis was introduced in [26].

Optimal location of FACTS devices is a complex
combinatorial analysis, which is best studied using
metaheuristic algorithms. Many researchers have tested
different optimization algorithms. A new meta-heuristic
algorithm called Cuckoo Optimization Algorithm (COA) was
developed in [27]. COA is a nature-inspired meta heuristic
algorithm which is inspired by the life of cuckoo bird family.
The special lifestyle of these birds and their characteristics in
egg-laying and breeding has been the basic motivation for
development of this new evolutionary optimization algorithm.
It is a novel evolutionary algorithm, suitable for the continuous
nonlinear optimization problem. Similar to other evolutionary
methods, the initial population of COA is randomly generated
within the control parameter limits. The effort to survive
among cuckoos constitutes the basis COA. During the survival
competition some of the cuckoos or their eggs may perish. The
survived cuckoo societies migrate to a better environment and
start reproducing and laying eggs. Cuckoos survival effort
hopefully converges to a state that there is only one cuckoo
society, with all birds having the best profit values. Application
of the COA algorithm to some benchmark functions and a real
problem has proven its capability in solving complex, nonlinear
and non-convex optimization problems [27]. The key features
of the COA are its faster convergence rate and the reduction in
computational complexity. Hence, it may become an effective
tool in solving power system optimization problems. However,
the COA is only introduced in the OPF problem [28], and it
still hasn’t been used to solve TCSC optimization problems. In
this paper, COA has been implemented to solve the OPF
problem which is formulated as a nonlinear optimization
problem with equality and inequality constraints in a power
system for maximization of the social welfare via optimal
installation of TCSC devices. The proposed approach has been
tested on the IEEE 14-bus and IEEE 30-bus systems.
Simulation results are compared with the re results of GA and
GWO and show that the COA is also one of useful algorithm in
solving the power system optimization problem.

II. PROBLEM FORMULATION

A. Modeling of TCSC

The model of the network with TCSC is shown in Figure 1.
TCSC is integrated in the OPF problem by modifying the line
data. This device may have either inductive compensation or
capacitive compensation by limiting 70% to 50% of the
reactance of the uncompensated line where TCSC is located.
Let Xij be the reactance of the transmission line and XTCSC the
reactance of TCSC and Xnew the new reactance of the line after
placing TCSC between buses i and j:

New ij TCSCX X X= + (1)

TCSC TCSC ijX k X= (2)

2
= ( cos sin )

ij i ij i j ij ij ij ij
P V G VV G Bδ δ− + (3)

2
= ( sin cos )

ij i ij i j ij ij ij ij
Q V B VV G Bδ δ− − − (4)

2
= ( cos sin )

ji j ij i j ij ij ij ij
P V G VV G Bδ δ− − (5)

2
= ( sin cos )

ji j ij i j ij ij ij ij
Q V B V V G Bδ δ− + + (6)

where δij is the voltage angle difference between bus i and bus,;
the conductance and susceptance of transmission line can be
calculated respectively as:

2 2

new

R
G

R X
=

+
(7)

new

2 2ij

ij ij

X
B

R X
=

+
(8)

jxr ijij+

jB
sh

jx
TCSC

Fig. 1. Modeling of transmission line with TCSC

B. Objective Function

Market prices for a given amount of power can be
determined by solving the optimization problem with the
objective of maximizing social welfare to satisfy limited
constraints. Generally, bulk loads as well as retailers in
deregulated electricity market are required to bid their
maximum demand and price function. Similarly, all generators
are also required to bid their generation cost function along
with their maximum generation. In electricity market,
generation and distribution companies are allowed to offer and
bid their prices to the ISO [29]. Social welfare optimization
provides the demand and the generation of all the buses to be
known. Let the vector of pool real power demand (Pdp) and

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vector of pool real power generation (Pgp) be given in (9) and
(10):

{ }; 1,2,3.....p PjPd Pd j m= = (9)

{ }; 1,2,3.....p PiPg Pg i n= = (10)
where, m is the number of dispatch able loads, and n is the
number of generators. Let the generation cost curve of the
generator placed at bus i bidding to the pool be denoted by

( )P
ii

PgC . The benefit function for a load is ( )P
jj

PdB . It

represents the load price which is willing to pay for the

purchase of an amount of electric power p
j

Pd . In electricity

market, the social benefit for an elastic load is given by (11).
The elastic load is sensitive to the energy price.











+ ∑∑

∈∈

)()(
j

i
PdWPgWMax

(11)

where Wj(Pdj) is the consumers welfare function. Optimal
social welfare occurs when the total of all generator and
consumer units’ welfare in the system are maximized.

( ) ( )
jjjjj

PdPdBPdW λ−=

(12)

The Bj in (12) indicates the i-th load utility function and λ is
the amount of cost that should be paid for each MW of energy
per unit. Wi(Pgi) is the welfare function of the generators:

( ) ( )
iiiii

PgCPgPgW −= λ (13)

Ci is representing the cost function of the i-th generator.
The λ is the cost each generator should be paid per MW of
energy. From (11)-(13) the objective function can be written as:

( ) ( )

d g

obj j j i i

i N i N

F Max B Pd C Pg
∈ ∈

 
 = −
 
 
∑ ∑ (14)

where, ( )
gigigigìgi

ii
cPbPaPgC ++= 2 is the cost function of the

generator and ( )
djdjdjdjdj

jj
cPbPaPdB ++= 2 is the profit

function of the customer.

The social welfare is mathematically maximized subject to
the following transmission network constraints:

• Power balance equation:

( , ) 0 1,...,i di gi bP V P P i Nδ + − = = (15)

( , ) 0 1,...,
i di gi b

Q V Q Q i Nδ + − = = (16)

• Power generation limit :

min max
1,.....,gi gi gi gP P P i N≤ ≤ = (17)

min max
1,.....,gi gi gi gQ Q Q i N≤ ≤ = (18)

• Bus voltage limits:

min max
1,.....,i i i bV V V i N≤ ≤ = (19)

• Apparent line flow limit:

,max 1,.....,l l lS S l N≤ = (20)

III. INTRODUCTION OF COA

COA is inspired by the special life style of cuckoo birds.
No cuckoo bird nests its eggs. Mature cuckoos have to find a
host bird nest to safely place their eggs. After that, the feed
responsibility belongs to the host bird. Only a number of the
cuckoo’s eggs have the chance to grow and become mature
cuckoos. All mature cuckoos will move forward to the best
Habitat. After some iterations, the cuckoo populations will
converge in a Habitat with the best profit values [27]. Like
other evolutionary algorithms, the proposed algorithm starts
with an initial population of cuckoos. These initial cuckoos lay
some eggs in some host bird’s nests. Some of these eggs which
are more similar to the host bird’s eggs have the opportunity to
grow and become mature cuckoos. Other eggs are detected by
the host birds and are destroyed. The grown eggs reveal the
suitability of the nests in that area. The more eggs survive in an
area, the more profit is gained in that area. So, the Habitat in
which more eggs survive will be the term that COA is going to
optimize.

A. Generating the Initial Cuckoo Habitat

In order to solve an optimization problem, it is necessary
the values of problem variables to be formed as an array. In
COA, it is called Habitat. In the Nvar dimensional optimization
problem, a Habitat is an array of 1×Nvar, representing the
current living Habitat of cuckoo. This array is defined as:

Habitat = [x1, x2, . . . , xNvar]T (21)

Each of the variable values (x1, x2, …, xNvar) is a floating
point number and a Habitat may represent a vector of control
variables of the OPF problem. The profit of a habitat is
obtained by the evaluation of the profit function fP at a Habitat.

Profit = fp(Habitat) = fp(x1, x2, . . . , xNvar ) (22)

COA is an algorithm that maximizes the profit function. In
order to use COA in cost minimization problems such as
minimizing the fitness function in the OPF problem, (22) can
be write as:

Profit = − Cost(Habitat) = − fp(x1, x2, . . . , xNvar )(23)

B. Cuckoo’s Style for Egg Laying

In the first iteration, a candidate Habitat matrix of size
NPop×NVar is generated. Then some random eggs are dedicated
to each cuckoo and its ELR (Eggs Laying Radius) is calculated.
The ELR is defined as:

ELR = � ∗
� !"#$ %& ' $$#() * '+%%,- #..-

/%)01 ( !"#$ %& #..-
∗ (23456 − 234789) (24)

where α is an integer to handle the maximum value for ELR
and varhi and varlow is the up and down limits of optimal
variables. The aim of ELR is to determine and limit the
searching space in each iteration step.

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C. Eliminating Cuckoos in Worst Habitats

Due to the equilibrium in bird’s population, only a
maximum number of cuckoos may live in the environment,
termed as MaxNumofCuckoos. A priority list may be created
by evaluation and sorting of the Profit value of the Habitat of
each newly grown cuckoo. So, there are MaxNumofCuckoos
cuckoos from the first of priority list alive, and the other
cuckoos will die. This work will decrease computational time
because there is a limited number of best solutions to be used in
the next iteration.

D. Immigration of Cuckoos

The Habitat in which cuckoos have the best conditions to
live and grow or the best profit value will be considered as the
goal point of the other cuckoos. They will immigrate as closer
as they can towards the goal point. After a period of time,
cuckoos grow to mature cuckoos and restart the process. This
means that cuckoo population will find the best place to live
after many iterations. This work will help the OPF problem to
find the best solutions.

IV. APPLICATION COA FOR SOLVING THE PROBLEM OF
SOCIAL WELFARE MAXIMIZATION

The flow chart of COA for the social welfare maximization
problem is presented in Figure 2.

- Read data input

- Set parameter of COA

- Calculated egg laying radius (ELR) for each cuckoo

as (29-30)

- Update egg’s positions after laying eggs as (31-32).

Create the initial population of COA as (25-27 )

- Sort value of all fitness functions as a priority list and
stores the relevant each cuckoo

- Keep a number of MaxNumofCuckoos cuckoos and
kill the others at the bottom of list

Evaluate fitness function for each cuckoo as (33)

- Determine the best cost and the goal point

- Update new values to each cuckoo as (34)

Iter < Iter max

Output: the best cost and the goal point

Calculate the number of eggs for each cuckoo as (28)

Start

End

Yes

Fig. 2. The flowchart of COA for the social welfare maximization
problem

The steps of the maximizing social welfare problem using
the proposed COA are presented below.

Step 1: Prepare a system data base. System topology, line
and load specifications, generation limits, line flow limits and
cost coefficient parameters.

Step 2: Set parameter for COA and social welfare problem:
NumCuckoos: the number of cuckoos in the first population,
MinEggs: the minimum number of eggs of each cuckoo,
MaxEggs: the maximum number of eggs of each cuckoo,
MaxIter: the maximum number of iterations, MotionCoceff: the
variable to control the towards to goal point process,
MaxCuckoos: the maximum number of Cuckoos that can live at
the same time, RadiusCoceff: the control parameter of egg
laying radius, Npar is the number of optimal variables. It is set
equal to the number of variables included in vector Xid. Kp, Kq,
Kv, Ks: the penalty factors.

Step 3: Create the initial population:

2 2 1
.... , .... , .... , ,

id g gNg d dNd g gNg TCSC TCSC
X P P P P V V N K = 

(25)

Each Habitat of cuckoos (Xid) is created as follows:

( )min max min1*id id id idX X rand X X= + − (26)

A random goal point is created as follow:

( )min max minint 1*id id idGoalPo X rand X X= + − (27)
The Habitat is a random matrix sized [1xNpar], and is

representing the living environment of each cuckoo.

Step 4: Calculate the number of eggs for each cuckoo as:

( )
’

– 2

NumberCuckoo s eggs

MaxEggs MinEggs xrand MinEggs

+
(28)

Step 5: Calculate the ELR for each cuckoo. Update egg’s
positions after laying eggs.

( )max min
max

' id id
i

numbercuckoo s eggs X X RadiusCoeff
ELR

Total Number of egg

∗ − ∗
= (29)

max
* 3i iELR ELR rand= (30)

where rand3 is a random matrix with size 1xNumber of current
eggs, so ELRi is a matrix with number of eggs rows and Npar
columns.

( ) ( ) ( )( )41 cos sinrandi i iAdd ELR in angles ELR angles= − ∗ ∗ + ∗ (31)
( )1
id id iX X Add= + (32)

where rand4 is a random value, it can be set to 1 or 2, and
angles is a random line space represent for the flying angles of
cuckoo. Each row of matrix Xid is a candidate for the vector
habitat Xid. Then, the limit for each Xid is checked and the egg
laying process is done.

Step 6: Solve power flow for each candidate Xid. The fitness
function is calculated by:

lim 2 lim 2

1 1

lim 2 max 2

1 1

NB NB

f obj p gi gi q gi gi

i i

NB NL

V i i S li li

i i

F F k (P P ) k (Q Q )

k (V V ) k (s S )

= =

= − − − −

− − − −

∑ ∑

∑ ∑
(33)

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Step 7: Evaluate the fitness function for each Xid in Step 6.
Sort the value of all fitness functions as a priority list and store
the relevant Xid.

Step 8: Based on the priority list, keep a number of
MaxNumofCuckoos Xid and kill the others at the bottom of the
list.

Step 9: The first Xid of the list is the best Xid solution in this
iteration. It is the best cost and will be the new goal point for
the others. Their new Habitat is determined as:

( ) ( )( ) ( )2 1 1int- * 5*id id idX Goalpo X rand MotionCoeff X= + (34)
Step 10: Update new values to Xid and save the best cost,

which is the goal point.

Step 11: Check the condition to stop the program. If
Iter < IterMax, Iter = Iter + 1 and return to Step 4. Otherwise, stop.

V. NUMERICAL RESULTS

A. IEEE 14-Bus Test System

The IEEE 14-bus system was used to investigate the effect
of TCSC on social welfare. The IEEE 14 bus system consists
of 5 generators and 20 lines, as shown in Figure 3. The
marginal benefit function for generator and load are given in
[12]. Optimal power flow programs are executed by modifying
the MATPOWER [30] program implementation of COA in
scheduling GENCOS and DISCOS (Table I).

Fig. 3. The IEEE 14-bus system

Fig. 4. The bus voltage profile of IEEE 14-bus system with and without
TCSC

Fig. 5. Power flow branch of IEEE 14-bus system with and without TCSC

The results of social benefit, scheduling of GENCOS and
DISCOS in the case of with and without TCSC for the IEEE 14
bus system are presented in Tables I-IV. From Table I it can be
seen that, the total real power of the generator and the total
power consumption in the case of using the COA algorithm are
higher than when using the GA and GWO algorithm [22].
Moreover, the distribution of power consumption at the load
buses of the COA algorithm compared to GA, GWO is also
different, reflecting in better social benefit value for COA
algorithm as shown in Table III.

Fig. 6. Convergence characteristics of COA compared PSO and BOA for
the IEEE 14 bus system without TCSC

Fig. 7. Convergence characteristics of COA compared PSO and BOA for
the IEEE 14 bus system with TCSC

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TABLE I. COMPARISON OF GA AND GWO SCHEDULING OF GENCOS AND DISCOS WITHOUT TCSC FOR THE IEEE 14 BUS SYSTEM

Bus

GA [22] GWO [22] COA

V (pu) P (MW) Q (Mvar) V (pu) P (MW) Q (Mvar) V (pu) P (MW) Q (Mvar)

Gen 1 1.1 94.97 45.43 1.1 97.55 43.51 1.1 97.675 39.895

2 1.089 100.0 56.58 1.089 100.0 54.57 1.091 100.00 59.818

3 1.095 100.0 29.86 1.095 100.04 29.18 1.100 100.00 34.050

6 1.035 52.08 7.22 1.035 50.31 15.29 1.027 52.176 10.825

8 1.09 0 25.28 1.09 0 25.21 1.086 0 24.995

Total 347.0 164.67 347.9 167.76 349.8 169.58

Dis 4 0.997 110.9 53.75 0.998 110.9 53.73 0.998 110.11 53.330

5 0.991 131.3 63.61 0.994 117.6 56.99 0.993 118.79 57.536

9 1.039 5.01 2.43 1.04 5.02 2.43 1.045 0 0

10 1.019 20.82 10.08 1.022 11.15 5.4 1.034 5.0015 2.4223

11 1.01 18.19 8.81 1.0 29.92 14.49 1.015 13.897 6.7306

12 0.998 18.51 8.97 0.978 31.35 15.18 0.993 28.420 13.764

13 1.01 14.42 6.98 1.01 5.63 2.73 0.970 31.485 15.249

14 1.009 12.07 5.85 0.998 19.51 9.45 1.002 5.0000 2.4216

Total 331.3 160.49 331.16 160.39 332.83 161.20

TABLE II. COMPARISON OF GA AND GWO SCHEDULING OF GENCOS AND DISCOS WITH TCSC FOR THE IEEE 14 BUS SYSTEM

Bus

GA [22] GWO [22] COA

V (pu) P (MW) Q (Mvar) V (pu) P (MW) Q (Mvar) V (pu) P (MW) Q (Mvar)

Gen 1 1.1 98.37 53.65 1.1 93.83 44.26 1.1 94.903 32.391

2 1.089 100.1 53.66 1.089 101.1 52.95 1.093 100.03 59.480

3 1.095 100.0 30.1 1.095 101.1 28.42 1.099 100.00 28.517

6 1.035 64.25 7.92 1.035 49.8 15.42 1.051 49.492 19.235

8 1.09 0 25.49 1.09 0 26.0 1.092 0 24.987

Total 362.8 170.82 344.8 344.87 344.43 164.61

Dis 4 0.997 125.4 60.74 0.999 102.8 49.79 1.000 116.8 56.60

5 0.995 129.1 62.54 0.994 118.7 57.71 0.997 117.6 56.97

9 1.039 5.0 2.42 1.036 5.0 2.42 1.038 5.001 2.422

10 1.019 20.12 9.74 1.019 14.46 7.0 1.019 22.14 10.72

11 1.007 20.48 9.92 1.001 26.95 13.05 1.014 20.13 9.749

12 0.995 27.99 13.55 0.981 27.71 13.42 1.014 22.03 10.67

13 1.012 10.5 5.09 1.002 8.57 4.15 1.019 11.45 5.546

14 1.016 7.69 3.72 0.985 24.14 11.69 0.996 22.85 11.06

Total 346.3 167.74 328.37 159.04 328.1 158.88

TABLE III. COMPARISON OF GA, GWO AND COA FOR SOCIAL WELFARE MAXIMIZATION FOR THE IEEE 14 BUS SYSTEM

Without TCSC With TCSC

GA [22] GWO [22] COA GA [22] GWO [22] COA

Gencos 1408.93 1415.50 1424.87 1494.77 1401.62 1396.48

Discos 2910.75 2966.62 2982.17 3014.85 2969.66 3022.30

Social Welfare 1501.81 1551.12 1557.30 1520.08 1568.03 1581.21

Location of TCSC Line 1-5 Line 6-13 Line 7-9

Size of TCSC (pu) -0.2315 -0.49 -0.693

Table III shows that the social benefit of GA and GWO
algorithms is 1501.81 ($/h) and 1551.12 ($/h) while for COA is
1557.30 ($/h). Compared with GA and GWO, the social benefit
of COA is 3.56% higher than the one for GA and 0.39% higher
than the one for GWO. In addition, as can be seen from Figures
4-5, the power on the branches and the voltage at the buses
when using the COA algorithm are within the allowable limits.
The scheduling of GENCOS and DISCOS in the case with
TCSC of COA are presented in Table II. The TCSC has
redistributed the power flow on the lines, increasing social
benefits. The optimal position of TCSC is at line 7-9 with
XTCSC=-0.693pu when using the COA algorithm. From Figures
3-4 it can be seen that the power flow on the branches in the

system is redistributed with more balance, the voltage at the
buses is also within limits after installing TCSC. Social benefits
of GA, GWO and COA algorithms with TCSC are presented in
Table III. It can be seen that the social benefit in the case when
using TCSC of COA algorithm is 3.86% higher than with GA
algorithm with TCSC and 0.83% higher than with GWO
algorithm with TCSC. The results of generator power and load
power cases with and without TCSC using COA algorithm are
presented in Table IV. From this Table, it can be seen that the
total real power of generator and total power consumption in
the case of TCSC is less than in the case without TCSC, but the
social benefits in the case of TCSC are higher than without
TCSC as shown in Table III. This shows that TCSC has

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improved social benefits. The TCSC has redistributed the
power flow and improved the transmission capability. Hence,
load buses that have high benefit factor tend to increase the
power consumption as seen in Table IV (bus 10, bus 14), while
load buses that have low benefit tend to reduce power
consumption as seen in Table IV (bus 11, bus 4), so customer
benefits are increased and results of social benefits in the case
with TCSC is 1.51% higher than when there is no TCSC. In

addition, the convergence of the COA algorithm is compared to
Particle Swarm Optimization (PSO) and Butterfly Optimization
Algorithm (BOA). From Figures 6-7 can be seen that COA has
the ability to converge quickly when compared to PSO and
BOA. This shows that the COA algorithm is able to find the
suitable location and size of TCSC to improve social benefits in
the electricity market. It also shows the ability of the proposed
COA algorithm to converge.

TABLE IV. THE RESULTS OF SCHEDULING OF GENCOS AND DISCOS WITH AND WITHOUT TCSC FOR THE IEEE 14 BUS SYSTEM

COA
Without TCSC With TCSC

Bus no Voltage (pu) Real power (MW) Reactive power (Mvar) Voltage (pu) Real power (MW) Reactive power (Mvar)

Gencos 1 1.1 97.6759 39.8956 1.1 94.9034 32.3914

2 1.0911 100.0001 59.8188 1.0935 100.0353 59.4800

3 1.1000 100.0003 34.0500 1.0999 100.0024 28.5171

6 1.0271 52.1765 10.8259 1.0511 49.4929 19.2359

8 1.0862 0 24.9951 1.0924 0 24.9875

Total 349.8529 169.5854 344.4340 164.6120

Discos 4 0.9983 110.1130 53.3301 1.0050 103.1062 49.9366

5 0.9932 118.7988 57.5369 1.0011 115.3352 55.8594

7 1.0456 0 0 1.0521 0 0

9 1.0343 5.0015 2.4223 1.0410 5.0037 2.4234

10 1.0151 13.8970 6.7306 1.0227 22.2554 10.7788

11 0.9939 28.4203 13.7646 1.0178 19.7659 9.5731

12 0.9700 31.4859 15.2493 0.9954 30.8817 14.9567

13 1.0027 5.0000 2.4216 1.0255 5.0174 2.4301

14 0.9905 20.1220 9.7455 1.0063 26.6867 12.9250

Total 332.8384 161.2010 328.0524 158.8830

TABLE V. COMPARISON OF GA AND GWO SCHEDULING OF GENCOS AND DISCOS WITHOUT TCSC FOR THE IEEE 30 BUS SYSTEM

Bus

GA [22] GWO [22] COA

V (pu) P (MW) Q (Mvar) V (pu) P (MW) Q (Mvar) V (pu) P (MW) Q (Mvar)

Gen 1 1.0 180.0 - 40.2 1.0 178.0 -39.78 1.0 192.5 8.253

2 1.0 53.19 54.31 1.0 60.29 52.42 0.977 79.67 37.74

5 1.0 35.32 89.76 1.0 33.61 91.46 0.947 32.56 70.01

8 1.0 35.0 53.43 1.0 34.99 53.21 0.953 19.66 54.63

11 1.0 30.0 12.69 1.0 30.0 12.09 0.997 27.48 15.84

13 1.0 40.0 28.27 1.0 40.0 32.06 0.999 39.35 20.74

Total 373.5 198.05 376.9 201.48 391.3 207.2

Dis 2 1.000 50.0 24.22 1.000 50.0 24.22 0.977 49.98 24.20

3 0.984 8.82 4.27 0.984 9.7 4.7 0.956 3.647 1.766

4 0.982 8.51 4.12 0.982 2.02 0.98 0.946 9.927 4.807

5 1.000 100.0 48.43 1.000 100.0 48.43 0.947 99.94 48.40

7 0.974 46.31 22.43 0.972 49.14 23.80 0.925 50.00 24.21

8 1.000 34.12 16.52 1.000 33.39 16.46 0.953 50.00 24.21

10 0.959 9.36 4.53 0.961 4.25 2.06 0.950 8.390 4.063

12 0.962 33.91 16.42 0.957 49.96 24.2 0.972 19.20 9.303

14 0.941 8.31 4.02 0.942 3.6 1.74 0.942 10.00 4.843

15 0.942 5.72 2.77 0.935 9.89 4.79 0.937 9.885 4.787

16 0.949 9.10 4.41 0.955 2.41 1.17 0.954 6.738 3.263

17 0.953 4.76 2.31 0.958 3.18 1.54 0.950 2.894 1.401

18 0.927 6.5 3.15 0.929 7.91 3.83 0.918 6.122 2.965

19 0.928 8.37 4.05 0.936 2.34 1.13 0.915 9.854 4.772

20 0.934 2.96 1.44 0.941 2.02 0.98 0.921 5.526 2.676

21 0.953 6.06 2.91 0.952 11.61 5.62 0.943 6.340 3.070

23 0.936 4.91 2.38 0.926 8.08 3.91 0.921 9.830 4.760

24 0.943 3.45 1.67 0.935 6.55 3.17 0.927 5.408 2.619

26 0.938 2.01 0.87 0.936 2.09 1.01 0.913 3.266 1.581

29 0.931 3.45 1.67 0.940 2.06 1.000 0.913 3.001 1.453

30 0.922 6.57 3.18 0.932 5.59 2.71 0.901 7.499 3.632

Total 363.1 175.87 366.38 177.45 377.4 182.8

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B. IEEE 30-Bus Test System

The IEEE 30 bus data are considered from [31]. The system
has 6 GENCOS and 21 DISCOS with 41 transmission lines, as
shown in Figure 8. The marginal benefit function for GENCOS
and DISCOS are given in [31]. The implementation of COA in
scheduling GENCOS and DISCOS in the case without TCSC
is presented in Table V. The Table shows that the total real
power of generator and total power consumption when using
the COA algorithm are higher than when using GA and GWO
algorithms [22].

Fig. 8. The IEEE 30-bus system

Fig. 9. The bus voltage profile of IEEE 30-bus system without and with
TCSC

The scheduling is different reflecting in better social
benefit, which is shown in Table VI. Using GA and GWO
algorithm, the social benefit is 5098.72 ($/h), and 5116.56
($/h), and that of COA is 5771.90 ($/h), which is 11.66% and
11.35% higher respectively. Figures 9-10 show the power on
the branches and the voltage at the buses in the case without

and with TCSC when using the COA algorithm, and they meet
the allowable limits. It can be seen that, the social benefit value
of using COA with TCSC is 5828.29 ($/h) as shown in Table
VI, which is 12.28% higher than the social benefit of using GA
with TCSC, and is 6.66% higher than the social benefit of
using GWO with TCSC. From Figures 11-12 it can be seen that
in the case with TCSC, COA has the ability to converge
quicker than PSO and BOA. This shows that the COA is one of
the useful methods for TCSC installation to maximize social
welfare.

Fig. 10. Power flow branch of IEEE 30-bus system without and with TCSC

Fig. 11. Convergence characteristics of COA compared with PSO and
BOA for the IEEE 30 bus system without TCSC

Convergence characteristics of COA compared with PSO and BOA for the
IEEE 30 bus system with TCSC

P
o
w
e
r
F
lo
w
i
n
B
r
a
n
c
h
[
M
V
A
]

Engineering, Technology & Applied Science Research Vol. 9, No. 6, 2019, 4946-4955 4954

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TABLE VI. COMPARISON OF GA, GWO AND COA FOR SOCIAL WELFARE MAXIMIZATION FOR THE IEEE 30 BUS SYSTEM

COA
Without TCSC With TCSC

GA [22] GWO [22] COA GA [22] GWO [22] COA

Gencos 1133.95 1144.84 1392.7028 1123.76 1250.19 1404.7130

Discos 6232.68 6261.40 7164.8892 6235.99 6689.80 7233.0322

Social Welfare 5098.72 5116.56 5771.9023 5112.22 5439.61 5828.2939

Location of TCSC Line 6-28 Line 6-8 Line 1-2

Size of TCSC (pu) -0.4366 0.5 0.4999

VI. CONCLUSIONS

Maximizing social welfare is one of the most important
issues in today’s competitive electricity market and a difficult
challenge for the operator system to implement. Maximizing
social welfare depends on the optimal rescheduling of
generation, demand levels, and optimal placement of TCSC. In
order to solve this problem, an effective method is required. In
this paper, the Cuckoo Optimization Algorithm was proposed
to maximize social welfare via optimal placing and sizing of
TCSC. The test results on the IEEE 14-bus and the IEEE 30-
bus systems when utilizing COA were compared with the
results from GA and GWO. The obtained simulation results
demonstrate that the COA is a useful method for TCSC
installation to maximize social welfare.

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