Genetic Algorithm Based Optimal Coordination of ... 7 No 10/Geneti… · current setting multiplier...
Transcript of Genetic Algorithm Based Optimal Coordination of ... 7 No 10/Geneti… · current setting multiplier...
International Electrical Engineering Journal (IEEJ)
Vol. 7 (2017) No.10, pp. 2403-2414
ISSN 2078-2365
http://www.ieejournal.com/
2403 Kheirollahi et. al., Genetic Algorithm Based Optimal Coordination of Overcurrent Relays Using a Novel Objective Function
Abstract—Power system protection includes numerous types of
optimizations implemented to increase the level of stability
and secure the electrical network. There are two significant
components in determining and choosing optimizing
algorithms in protective functions: the precision of the output
results and reducing execution time of the optimization
algorithm. This paper presents a novel approach to optimize
overcurrent relay coordination in power systems. Proposing a
novel Objective Function (OF) is the main concern of this
paper which ultimately decreases the value of operating time
in relays and the execution time. This item is of major
importance to improve network’s protection and stability. The
proposed OF is able to be employed in other overcurrent relay
coordination problems. To show the correctness of the
suggested approach, it is applied to two standard power
networks. S imulation results proves the accuracy and
usefulness of the proposed strategy in comparison with
previous studies.
Index Terms— Genetic algorithm, Optimization methods,
Overcurrent protection, Power system protection.
I. INTRO DUCTIO N
Modern power systems are prone to extending over a wide
area of failures. Owning to the fact that power demand is
increased, the operation, stability, protection, and planning of
large interconnected power system are becoming more and
more complex, so it will be less secure system [1]. The electrical
energy transmission lines, as a considerable part of a power
system, have a significant part in the field of stability and
satisfactory operation of system. This part of the network
often falls under the effect of various faults and leads to the
increase of the currents in upper levels. If these faults are not
removed in time, they cause loss of the stability, damage the
equipment of the system and blackout the network.
Hence, the fundamental role of protecting functions in
protective systems is detecting faults timely and correctly and
then isolating them from other parts of the network as soon as
possible. In this case, the impact to the rest of the system is
minimized, leaving intact as many non-faulted elements as
possible. As different protective relays are used in different
voltage levels of the power network, the directional
overcurrent relays (DOCRs) are widely implemented in power
systems as the main protection devices in distribution grids
and backups for distance relays in transmission and sub
transmission lines. They can also be used as backup
protection devices for power transformers and generators.
The purpose of coordinating DOCRs is to adjust settings in
order that it minimizes the operation time for faults within the
protective zone; besides, it offers pre-definite timed backup for
relays at the same time which are in the adjacent zones [2]. As
the primary protection system may fail (relay fault or breaker
fault), protection must act as backup either in same station or
in neighboring lines without much delay in operating time
according to the necessary requirements [3].
Regarding the time delay operation, DOCRs are categorized
as the definite time and inverse time types. Inverse time relays
are extensively used where a smaller delay is essential in order
to minimize the equipment damages related to intensive faults
near power supplies. However, coordinating the inverse time
relays is more complicated, and it sounds a time-consuming
process. DOCRs are usually coordinated offline within the
power network being in the dominant utilization topology [4].
They are usually adjusted based on time-current
characteristics of relays which can be determined based on
IEC standard characteristics. Generally, the range of the
current setting multiplier in DOCRs varies from 50 to 200 % in
steps of 25% referred to Plug Setting (PS). The PS is quantified
between the maximum load current and the minimum of the
fault current passing through the relay. Time Setting
Genetic Algorithm Based Optimal
Coordination of Overcurrent Relays
Using a Novel Objective Function
R. Kheirollahi1, R. Tahmasebifar2, E. Dehghanpour3 1Faculty of Electrical & Computer Engineering, Tarbiat Modares University, Tehran, Iran.
[email protected] 2Faculty of Electrical & Computer Engineering, Tarbiat Modares University, Tehran, Iran.
[email protected] 3Faculty of Electrical Engineering, Shahid Beheshti University, Tehran, Iran
International Electrical Engineering Journal (IEEJ)
Vol. 7 (2017) No.10, pp. 2403-2414
ISSN 2078-2365
http://www.ieejournal.com/
2404 Kheirollahi et. al., Genetic Algorithm Based Optimal Coordination of Overcurrent Relays Using a Novel Objective Function
Multipliers (TSM) are the most important setting in the optimal
coordination of overcurrent relays. Appropriate coordination
between relays in various conditions plays a serious part in
performance of protection systems to lessen the de-energized
region [5].
Over the past five decades, several studies on optimal
coordination of overcurrent relays have been carried out.
These studies can be divided into three categories: 1) Trial and
error method 2) Structural analysis method 3) Optimization
method. Due to the complexity of non-linear programming
methods, optimal coordination methods such as simplex,
two-simplex and dual simplex have been used [6-11]. Also,
because of their nonlinearity, manual coordination has been
formulated as an optimization problem, and several
optimization methods such as deterministic, heuristic, and
hybrid have been proposed to solve it. Artificial intelligence
methods and nature-inspired algorithms such as linear
Programming [12-14], Particle Swarm Algorithm (PSO) [15],
Genetic Algorithm (GA) [16-21], hybrid GA and mixed PSO
[22-23], Bat Optimization Algorithm (BOA) [24] among others
are used to solve the issue of optimal coordination of
overcurrent relays. Also, Mahari and Seyedi [25] have
proposed a new analytic approach to solve the optimal
coordination of DOCRs.
Although many researches were presented to optimize the
coordination of DOCRs, employing a well-formulated
Objective Function (OF) plays the noteworthy feature in the
reported methods. In some cases, choosing improper OF
prevents optimization algorithms to reach to the optimum
answers. To avoid this, several improvements were reported,
and they are illustrated in the next sections. The main novelty
of this paper is proposing a novel OF with two important aims;
firstly, all the constraints of the problem are satisfied from
practical aspects; for example, the operating time difference
between primary and backup relays must be considered.
Secondly, the results are more optimized in comparison with
other proposed OFs. Regardless of the fact that the selected
optimization algorithm is GA in this brief, the proposed OF can
be employed in other coordination problem with different
optimization algorithms.
The rest of the paper is organized as follows: sections II
deals with the applications of the GA in the relay coordination;
section III presents the proposed approach; simulation results
are provided in section IV; followed by conclusion in section
V.
II. GENETIC ALGORITHM IN RELAYS COORDINATION
One of the best methods in optimal coordination of DOCRs
is using intelligent methods like GA. Previous studies have
presented so many discussions about the superiority of GA in
comparison with other techniques [9, 26-30]. The aim of
formulating the coordination of DOCRs as an optimization
problem is to minimize the operating time of primary and
backup relays, while keeping selectivity. Furthermore,
constraints related to time discrimination between primary and
backup relays pairs will be applied directly in the OF formula.
GA is widely employed in DOCRs coordination optimization
problem in the case of both continuous and discrete TSM [16,
31-33]. Chromosomes of GA include continuous TSM of
relays. Discrete TSM are found by rounding the continuous
TSM to the next allowable discrete values marked on the relay
at the end of each GA iteration. The main problem in optimal
coordination of DOCRs using GA (and also other optimization
techniques) is miscoordination between primary and backup
relays limiting the performance of the algorithm [9-30]. To
overcome this problem, the constraints related to the
operating time difference between primary and backup relays
are inserted to the OF formula. In this case, not only does the
operating time of the DOCRs are minimized, but also the
miscoordination will be solved.
Reported intelligent methods using GA [9, 16, 26, and 31]
have presented several OFs which are generalized in the
following equation:
2
11
2
2 3 41
( * *( | |))
N
ii
P
mbk mbk mbkk
OF a t
a a t a t t
(1)
Where a1, a2, a3 and a4 are introduced as constant values
given in Table I; these coefficients get different values in the
aforementioned references which are stated in details in Table
I. The parameter N portrays the number of relays; P is the
number of primary and backup relays; the value of K
represents each primary and backup pair in which varies from 1
to P; the quantity of i represents each relay and varies from 1 to
N; it is operating time of i-th relay, mbkt is the operating time
difference between the primary and backup relay pairs defined
as mbk b pt t t CTI . In the mbkt formula, bt and pt are
the operating time of backup and primary relays respectively,
and CTI is the critical time interval in relay characteristics for
primary and backup relay pairs which is taken as 0.2 in this
paper. By considering Table I, parameters α1 and α2 are used to
control the weights, β2 is employed as a penalty factor and is
determined by applying the trial and error procedure [31].
Table I Parameters for general OF mentioned in [9, 26, 16, and 31]
Parameter Ref. [9,26] Ref. [31] Ref. [16]
a1
a2
a3
a4
α1=1
α2=2
1
0
α1=1
α2=2
1
β2=100
α1=1
α2=2
0
β2=100
International Electrical Engineering Journal (IEEJ)
Vol. 7 (2017) No.10, pp. 2403-2414
ISSN 2078-2365
http://www.ieejournal.com/
2405 Kheirollahi et. al., Genetic Algorithm Based Optimal Coordination of Overcurrent Relays Using a Novel Objective Function
The first term of the equation 1 is the operating time of relays
related to faults close to the circuit breaker of the main relays.
SO and Li (2000) introduced an OF that cannot solve the
problem of miscoordination; the reported OF does not consist
of penalty factor (a4=0). Razavi et al. (2008) offered the second
term of the OF to remove the miscoordination between relays
pair, but it introduces a redundant term obstruct ing
coordination from efficient optimization. Mohamadi et al.
(2010) modified the OF in order to show that the optimization
will be more efficient and optimal; in this case, if 0mbkt the
second part of the equation becomes zero, and the OF will not
be added by any amount, while if 0mbkt , the second term
of the equation becomes 2 2
2 2 (2* )mbkt ; Therefore, by
adding the mentioned term to the OF formula, the fitness of
chromosomes including miscoordination problem is abated.
III. PRO PO SED METHO D
In this section, the OF reported by Razavi et al. (2008) and
Mohamadi et al. (2010) are analyzed firstly. The OF stated by
SO and Li (2000) suffers from miscoordination problem, so it is
not regarded in our analysis. Second, by taking the flaws of the
aforementioned OFs into account, the modified OF is
proposed comprehensively.
The first term of the equation 1 is implemented to optimize
the operating time of relays, and it has gotten a same definition
as can be shown in Table I. The main concern is adding the
second term in a way that the miscoordination is solved, and
also the effectiveness of the optimization algorithm will not be
abated.
Several improvements of the OF was carried out by
Mohamadi et al. (2010) in comparison with OF proposed by
Razavi et al. (2008); however, it suffers from two significant
flaws which makes the selected optimization algorithm not to
be executed well. They are illustrated as follows:
1) The value of the coefficient 2 was defined as a constant
value for different electrical networks, and the appropriate 2
has been obtained by using the Trial and Error procedure.
Because choosing the optimum value of 2 based on the
Trial and Error procedure is a time-consuming process, this
value was designated as a large constant value, reported in
references [16] and [31]. Although a large amount of β2
prevents the miscoordination between primary and backup
relays, the effectiveness of the optimization algorithm process
is affected.
2) The second weakness related to the OF proposed by
Mohamadi et al. (2010) is that the penalty factor for all
miscoordination values is taken constant, while the difference
operating time in range 0.05 0mbkt was not reported
as miscoordination [31]. The question is: by regarding the
practical aspects of the DOCRs coordination, is the small
values of 0mbkt meant miscoordination?
Consider 0.02mbkt ; in this case, the difference operating
time between primary and backup relays is 0.18b pt t ,
taking the CTI=0.2 into account. Despite the fact that large
values of mbkt guarantee the operating time delay related to
the protective DOCRs and their peripheral equipment, another
aspect is optimizing the operating time of main relays. The
compromise solution may be the following statements: the
values of 0mbkt should be always considered as
miscoordination, but the penalty factor can be varied.
In view of the fact that the operating time difference with
values between 0.05 0mbkt can be neglected, and any
miscoordination is not defined in this range from practical
applications aspects [31], the chromosomes containing
operating time difference in range 0.05 0mbkt can be
allowed to transmit to the next generation, and their fitness for
selection as parents are not decreased. In this case, not only
does the miscoordination not occur, but also the accuracy of
output results, and the execution time of the algorithm are
improved markedly. To do this, the constant value of 2 is
replaced by a dynamic coefficient in this paper; consequently,
the improvement is attained, and the optimization algorithm
gets better answers. In order to exert the dynamic value of 2
2 2 in the OF, it is considered as the varied factor
introduced in Equation 2:
2 2
2 2m mbkt (2)
Thus the OF will be modified as following:
2 2
11 1
( | |)N P
i m mbk mbki k
OF t t t
(3)
Then, the GA executive routine will be changed based on the
modified OF, and the value of βm is determined dynamically.
Fitness of chromosomes including TSM within range
0.05 0mbkt are not decreased; in this way, they will be
contributed in the next generation of the algorithm. The flow
diagram of GA including new OF in optimal coordination of
DOCRs is graphically presented in Fig. 1.
International Electrical Engineering Journal (IEEJ)
Vol. 7 (2017) No.10, pp. 2403-2414
ISSN 2078-2365
http://www.ieejournal.com/
2406 Kheirollahi et. al., Genetic Algorithm Based Optimal Coordination of Overcurrent Relays Using a Novel Objective Function
By regarding the constant quantities for α2 and β2, the
penalty factor values of 2
2 2 and βm are different. The results
are shown in Table II. As shown in Table II, in the case of
0.05mbkt , both βm and 2
2 2 get large values, and the
miscoordinations are solved; however, for
0.05 0mbkt which can be neglected, the amount of
2
2 2 is large, but the value of βm will be inconstant and small.
By considering the proposed OF, the fitness of chromosomes
including TSM with range 0.05 0mbkt is not
decreased. This subject speeds up the optimization algorithm
procedure and decreases the operating time of relays in
optimal coordination of the DOCRs. Setting parameters related
to the presented GA are given in Table III.
Table II Values of 22 2 and βm in the case of α2=2, β2=100
mbkt 22 2
2 2
2 2m mbkt
- 0.01 20000 2
-0.05 20000 50
-0.1 20000 200
-0.5 20000 5000
Table III Parameters of GA
Population size
Fitness function
Selection function
Mutation
Crossover function
Initial penalty
Penalty factor
Creation function
Number of
generation
100
Rank
Stochastic uniform
1
scattered
30
400
use default dependent
default
300
IV. SIMULATION RESULTS
A. Case Study 1
Fig. 2 shows the IEEE 8-busbars test system consisting of 9
transmission lines, 2 transformers and 14 directional DOCRs.
All the DOCRs have IEC standard characteristics.
Fig. 2 IEEE 8-busbars test system.
Busbar no.4 has been connected to utility modelled by a
short-circuit capacity of 400 MVA. The system parameters are
the same as those have been mentioned by Bedekar and Bhide
[34]. The operating time of the DOCRs is formulated by
following Equation:
Yes
Yes
Initialization
2 2
1
1 1
( | |)N P
i m mbk mbk
i k
OF t t t
Parents Selection
I=1
Reproduction and Mutation
Population Size<Imax
Max Generation<Gmax
END
I=I+1
G=G+1
Fig. 1 Flow diagram of GA application in the case of optimal
coordination of DOCRs.
International Electrical Engineering Journal (IEEJ)
Vol. 7 (2017) No.10, pp. 2403-2414
ISSN 2078-2365
http://www.ieejournal.com/
2407 Kheirollahi et. al., Genetic Algorithm Based Optimal Coordination of Overcurrent Relays Using a Novel Objective Function
*
1
n
TSM
ISC
I
t
p
(4)
Where ISC and Ip introduce the values of short-circuit fault
currents and the PS in relays, respectively; the quantity of
TSM is defined in a continuous manner with respect to the
1-percent steps in relay characteristics. Short-circuit currents
passing through the primary and backup relays per every
symmetrical three phase short-circuit fault occurring near the
circuit breaker of the primary relay are included in App. A.
B. Results and discussion
In order to have a desirable functioning demonstration of the
proposed modified algorithm, The GA with distinctive OF and
different values of α1, α2, and β2 are applied to the optimal
coordination of overcurrent relays problem. In order to verify
the accuracy of the results, all the simulations have been
carried out on one computer and output results are shown in
Table IV. By comparing the execution time of the mentioned
algorithms and the accuracy of the output results, advantages
of the proposed method are proven. It should be noticed that
in the second and sixth column of the Table IV, the values of
the 1
( )N
it i
and the execution time are smaller than the
results of proposed method in the fifth and ninth column;
nevertheless, as it can be seen in Table V, this method suffers
from some miscoordinatons ( 0.05mbkt ) between P/B
relays, and it is not accepted by protective functions in
DOCRs. The values of 0.05mbkt can be neglected in
practical applications. The operating time difference for each
relays pairs are presented in Table V.
C. Case Study 2
As the second network, the IEEE 14-busbars system that
consists of 5 generators, 2 transformers, 20 transmission lines
and 40 directional DOCRs is considered to show the capability
of the proposed approach to solve the issue of optimal
coordination of overcurrent relays. The parameters employed
in the network are taken from Kamel and Kodsi [35]. The base
voltage and the base power of the system are 138KV and
100MVA, respectively. All DOCRs have the IEC standard
characteristics that have been explained in the previous case
study. Short-circuit calculations were carried out on the
system, and the results including the short-circuit currents
passing through main and backup relays for each occurrence
of the three-phase short-circuit fault near the main relay are
shown in App. B.
D. Results and Discussion
Genetic algorithm with selected values of α1, α2, and β2 was
applied to the system shown in Fig. 3, and results are shown in
Tables VI and VII. The efficiency of the proposed method is
obviously better than others by considering the calculated
execution time and the value of1
( )N
it i
. Also, the operating
time differences for each relays pair illustrated in Table VII
show that the proposed method does not consist of any
miscoordination. As mentioned above, although GA with OF
proposed by [9, 26] presents smaller execution time, it contains
several miscoordiantions ( 0.05mbkt ) between relays pair
that can be seen in Table VII.
Fig. 3 IEEE 14-busbars test system [35].
V. CONCLUSION
Protection and stability are significant issues in power
systems. Appropriate settings of DOCRs for various
conditions play an important role in isolating the faulted
section in power systems on time. Applying optimizing
algorithms to the problems existing in power systems leads to
profiting and increasing the security level of the networks. The
execution time of the algorithm and the precision of the output
results extracted from the algorithm are two determining
parameters in selecting optimization algorithms in protective
functions. The GA is a suitable method for optimal
coordination of DOCRs. not only does the modified OF
introduced in this paper solve the problem of miscoordination
in DOCRs, but also it decreases the operating time of the
relays. The proposed OF is able to be used in other
optimization algorithm. Therefore, it causes
International Electrical Engineering Journal (IEEJ)
Vol. 7 (2017) No.10, pp. 2403-2414
ISSN 2078-2365
http://www.ieejournal.com/
2408 Kheirollahi et. al., Genetic Algorithm Based Optimal Coordination of Overcurrent Relays Using a Novel Objective Function
improvements in protection and stability of the power
systems. Simulated results extracted from two case studies
show that the proposed approach is more optimal, efficient
and flexible in comparison with the previous methods.
Table IV Results for IEEE 8-busbars system
α1= 1, α2= 2, β2= 100 α1= 1, α2= 1, β2= 50
TSM
TSM
Ref.[9,26
]
TSM
Ref. [31]
TSM
Ref.[16]
TSM
Proposed
TSM
Ref.[9,26]
TSM
Ref.[31]
TSM
Ref.[16
]
TSM
Proposed
TSM1
TSM2
TSM3
TSM4
TSM5
TSM6
TSM7
TSM8
TSM9
TSM10
TSM11
TSM12
TSM13
TSM14
0.06
0.11
0.08
0.06
0.06
0.12
0.1
0.12
0.06
0.08
0.08
0.15
0.06
0.08
0.08
0.21
0.19
0.12
0.09
0.19
0.17
0.18
0.08
0.17
0.18
0.29
0.08
0.14
0.08
0.21
0.19
0.12
0.09
0.18
0.17
0.17
0.08
0.17
0.18
0.29
0.08
0.14
0.07
0.19
0.17
0.11
0.08
0.16
0.16
0.17
0.08
0.16
0.16
0.26
0.08
0.13
0.06
0.11
0.08
0.06
0.06
0.12
0.1
0.12
0.06
0.08
0.08
0.15
0.06
0.08
0.08
0.21
0.19
0.12
0.09
0.19
0.17
0.18
0.08
0.16
0.17
0.28
0.08
0.14
0.08
0.21
0.19
0.12
0.09
0.17
0.17
0.17
0.08
0.16
0.17
0.28
0.08
0.14
0.07
0.19
0.17
0.11
0.08
0.16
0.16
0.15
0.07
0.14
0.15
0.25
0.07
0.12
2
1( )
N
it i
= 1.33 4.89 4.27 2.78 1.33 4.77 4.109 2.29
Execution
T ime (sec) 3.92 s 56.48 s 48.69 s 5.32 s 3.92 s 56.48 s 48.69 s 5.32 s
Miscoordinatio
n Yes No No No Yes No No No
Table V The operating time difference for relay pairs of IEEE 8-busbars system
α1= 1, α2= 2, β2= 100 α1= 1, α2= 1, β2= 50
Δtmbk (s)
Δtmbk (s)
Ref.[9,26
]
Δtmbk (s)
Ref. [31]
Δtmbk (s)
Ref. [16]
Δtmbk (s)
Proposed
Δtmbk (s)
Ref.
[9,26]
Δtmbk (s)
Ref. [31]
Δtmbk (s)
Ref. [16]
Δtmbk (s)
Proposed
∆t 9-8
∆t 7-8
∆t 7-2
∆t 1-2
∆t 2-3
∆t 3-4
∆t 4-5
∆t 5-6
∆t 14-6
∆t 1-14
∆t 9-14
∆t 6-1
∆t 10-9
∆t 11-10
∆t 12-11
∆t 14-12
0.005
-0.022
-0.071
0.152
-0.071
-0.198
-0.221
-0.026
0.026
0.236
0.039
-0.103
-0.248
-0.162
-0.088
-0.061
0.052
0.238
0.01
0.085
0.007
0.041
0.008
0.084
0.326
0.292
0.03
0.073
0.042
0.044
0.014
0.041
0.079
0.266
0.01
0.085
0.007
0.041
0.008
0.111
0.353
0.292
0.03
0.036
0.042
0.044
0.014
0.041
0.079
0.205
0.018
0.016
-0.016
-0.007
-0.005
0.066
0.326
0.19
0.066
0.003
-0.001
-0.024
-0.013
0.043
0.005
-0.022
-0.071
0.152
-0.071
-0.198
-0.221
-0.026
0.026
0.236
0.039
-0.103
-0.248
-0.162
-0.088
-0.061
0.052
0.238
0.01
0.085
0.007
0.041
0.008
0.084
0.326
0.292
0.03
0.073
-0.001
0.027
0.017
0.069
0.079
0.266
0.01
0.085
0.007
0.041
0.008
0.139
0.38
0.292
0.03
0.001
0.001
0.027
0.017
0.069
0.028
0.26
0.018
0.016
-0.016
-0.007
-0.005
0.066
0.244
0.227
-0.002
0.003
-0.038
-0.008
-0.01
-0.011
International Electrical Engineering Journal (IEEJ)
Vol. 7 (2017) No.10, pp. 2403-2414
ISSN 2078-2365
http://www.ieejournal.com/
2409 Kheirollahi et. al., Genetic Algorithm Based Optimal Coordination of Overcurrent Relays Using a Novel Objective Function
∆t 13-12
∆t 8-13
∆t 5-7
0.128
-0.096
-0.015
0.021
0.049
0.064
0.021
0.011
0.064
0.104
0.011
-0.005
0.128
-0.096
-0.015
0.049
0.049
0.064
0.049
0.011
0.064
-0.009
-0.023
-0.005
Δtmbk <
-0.05 Yes No No No Yes No No No
Table VI Results for IEEE 14-busbars system
α1= 1, α2= 2, β2= 100 α1= 1, α2= 1, β2= 50
TSM TSM Ref.
[9,26]
TSM
Ref.[31]
TSM
Ref.[16]
TSM
Proposed
TSM Ref.
[9,26]
TSM
Ref.[31]
TSM
Ref.[16
]
TSM
Proposed
TSM1
TSM2
TSM3
TSM4
TSM5
TSM6
TSM7
TSM8
TSM9
TSM10
TSM11
TSM12
TSM13
TSM14
TSM15
TSM16
TSM17
TSM18
TSM19
TSM20
TSM21
TSM22
TSM23
TSM24
TSM25
TSM26
TSM27
TSM28
TSM29
TSM30
TSM31
TSM32
TSM33
TSM34
TSM35
TSM36
TSM37
0.11
0.07
0.1
0.1
0.05
0.08
0.08
0.11
0.12
0.13
0.09
0.07
0.09
0.13
0.12
0.13
0.16
0.1
0.1
0.09
0.1
0.1
0.11
0.14
0.11
0.17
0.08
0.1
0.06
0.06
0.07
0.08
0.05
0.12
0.1
0.06
0.06
0.17
0.12
0.19
0.15
0.1
0.12
0.13
0.16
0.23
0.18
0.15
0.1
0.15
0.19
0.2
0.21
0.26
0.17
0.23
0.21
0.24
0.29
0.28
0.34
0.19
0.29
0.26
0.2
0.12
0.06
0.17
0.17
0.07
0.22
0.14
0.09
0.06
0.16
0.1
0.18
0.12
0.1
0.09
0.13
0.12
0.22
0.16
0.13
0.1
0.15
0.1
0.19
0.21
0.25
0.17
0.21
0.21
0.21
0.29
0.22
0.34
0.17
0.28
0.06
0.2
0.12
0.06
0.11
0.17
0.07
0.22
0.12
0.09
0.06
0.15
0.09
0.16
0.11
0.09
0.08
0.12
0.11
0.2
0.15
0.12
0.09
0.14
0.09
0.17
0.19
0.22
0.16
0.19
0.2
0.19
0.27
0.21
0.32
0.16
0.26
0.06
0.19
0.11
0.06
0.1
0.16
0.06
0.2
0.11
0.08
0.06
0.11
0.07
0.1
0.1
0.05
0.08
0.08
0.11
0.12
0.13
0.09
0.07
0.09
0.13
0.12
0.13
0.16
0.1
0.1
0.09
0.1
0.1
0.11
0.14
0.11
0.17
0.08
0.1
0.06
0.06
0.07
0.08
0.05
0.12
0.1
0.06
0.06
0.16
0.12
0.18
0.15
0.1
0.12
0.13
0.15
0.22
0.17
0.14
0.1
0.15
0.18
0.2
0.21
0.26
0.17
0.23
0.21
0.24
0.29
0.27
0.34
0.18
0.28
0.25
0.2
0.12
0.06
0.17
0.17
0.07
0.22
0.14
0.09
0.06
0.16
0.1
0.18
0.12
0.1
0.09
0.13
0.12
0.22
0.16
0.13
0.1
0.15
0.1
0.19
0.21
0.25
0.17
0.21
0.21
0.21
0.29
0.22
0.34
0.17
0.28
0.06
0.2
0.12
0.06
0.11
0.17
0.07
0.22
0.12
0.09
0.06
0.14
0.09
0.16
0.11
0.09
0.08
0.11
0.11
0.19
0.15
0.11
0.09
0.13
0.09
0.17
0.18
0.22
0.15
0.19
0.19
0.19
0.26
0.21
0.3
0.16
0.24
0.06
0.18
0.11
0.06
0.1
0.15
0.06
0.19
0.11
0.08
0.06
International Electrical Engineering Journal (IEEJ)
Vol. 7 (2017) No.10, pp. 2403-2414
ISSN 2078-2365
http://www.ieejournal.com/
2410 Kheirollahi et. al., Genetic Algorithm Based Optimal Coordination of Overcurrent Relays Using a Novel Objective Function
TSM38
TSM39
TSM40
0.1
0.13
0.06
0.17
0.19
0.09
0.12
0.19
0.08
0.11
0.18
0.07
0.1
0.13
0.06
0.16
0.19
0.08
0.12
0.19
0.08
0.11
0.17
0.07
2
1( )
N
it i
= 3.68 12.89 10.66 6.21 3.68 12.47 10.66 4.39
Execution Time(sec) 8.23 s 146.35 s 115.14 s 11.87 s 8.23 s 146.35 s 115.14 s 11.87 s
Miscoordination Yes No No No Yes No No No
Table VII The operating time difference for relay pairs of IEEE 14-busbars system
α1= 1, α2= 2, β2= 100 α1= 1, α2= 1, β2= 50
Δtmbk (s)
Δtmbk (s)
Ref.[9,2
6]
Δtmbk (s)
Ref. [31]
Δtmbk (s)
Ref. [16]
Δtmbk (s)
Proposed
Δtmbk (s)
Ref.
[9,26]
Δtmbk (s)
Ref. [31]
Δtmbk (s)
Ref. [16]
Δtmbk (s)
Proposed
∆t 6-1
∆t 2-5
∆t 4-2
∆t 12-2
∆t 8-2
∆t 1-3
∆t 12-3
∆t 8-3
∆t 4-11
∆t 1-11
∆t 8-11
∆t 1-7
∆t 4-7
∆t 12-7
∆t 11-13
∆t 14-12
∆t 9-26
∆t 13-26
∆t 7-26
∆t 30-26
∆t 13-10
∆t 7-10
∆t 25-10
∆t 30-10
∆t 9-14
∆t 7-14
∆t 25-14
∆t 30-14
∆t 9-8
∆t 25-8
∆t 13-8
∆t 30-8
∆t 7-29
∆t 9-29
∆t 13-29
∆t 25-29
∆t 3-6
∆t 10-6
∆t 16-6
∆t 5-4
∆t 16-4
∆t 10-4
∆t 5-15
∆t 3-15
∆t 10-15
∆t 5-9
∆t 3-9
0.11
-0.028
0.015
0.014
0.137
-0.027
0.019
0.142
0.029
-0.018
0.152
0
0.047
0.047
-0.004
0.302
-0.166
-0.104
-0.075
1.155
-0.186
-0.156
-0.199
1.074
-0.157
-0.066
-0.109
1.163
-0.028
0.021
0.034
1.293
0.189
0.098
0.159
0.146
0.092
0.13
0.165
0.039
0.144
0.108
-0.03
0.001
0.039
-0.139
-0.108
0.302
0.131
0.12
0.08
0.273
0.038
0.045
0.238
0.156
0.108
0.309
0.147
0.195
0.154
0.193
0.588
0.042
0.01
0.034
0.871
0.027
0.05
0.04
0.888
0.153
0.145
0.135
0.982
0.344
0.325
0.312
1.173
0.443
0.451
0.419
0.433
0.53
0.271
0.476
0.496
0.444
0.239
0.341
0.343
0.084
0.056
0.058
0.066
0.019
0.023
0.149
0.096
0.015
0.068
0.015
0.04
0.113
0.113
0.101
0.029
0.154
0.063
0.019
0.021
0.034
0.058
0.895
0.101
0.125
0.009
0.962
0.38
0.416
0.3
1.254
0.395
0.315
0.407
1.269
0.443
0.406
0.419
0.326
0.55
0.252
0.556
0.566
0.514
0.21
0.366
0.308
0.01
0.09
0.032
0.005
-0.013
0.001
0.104
0.068
0.016
0.036
0.001
0.009
0.091
0.076
0.081
-0.001
0.101
0.03
-0.013
-0.021
0.015
0.026
0.942
0.072
0.083
-0.007
0.999
0.321
0.368
0.277
1.284
0.329
0.286
0.365
1.293
0.387
0.34
0.376
0.296
0.455
0.229
0.478
0.475
0.433
0.184
0.302
0.238
0.011
0.044
-0.02
0.11
-0.028
0.015
0.014
0.137
-0.027
0.019
0.142
0.029
-0.018
0.152
0
0.047
0.047
-0.004
0.302
-0.166
-0.104
-0.075
1.155
-0.186
-0.156
-0.199
1.074
-0.157
-0.066
-0.109
1.163
-0.028
0.021
0.034
1.293
0.189
0.098
0.159
0.146
0.092
0.13
0.165
0.039
0.144
0.108
-0.03
0.001
0.039
-0.139
-0.108
0.329
0.131
0.12
0.08
0.212
0.015
0.068
0.2
0.181
0.087
0.273
0.101
0.195
0.154
0.128
0.524
0.021
0.034
0.058
0.895
0.064
0.088
0.024
0.925
0.138
0.175
0.112
1.012
0.323
0.296
0.336
1.197
0.443
0.406
0.419
0.38
0.47
0.221
0.476
0.496
0.444
0.189
0.341
0.283
0.034
0.09
0.032
0.066
0.019
0.023
0.149
0.096
0.015
0.068
0.015
0.04
0.113
0.113
0.101
0.029
0.154
0.063
0.019
0.021
0.034
0.058
0.895
0.101
0.125
0.009
0.962
0.38
0.416
0.3
1.254
0.395
0.315
0.407
1.269
0.443
0.406
0.419
0.326
0.55
0.252
0.556
0.566
0.514
0.21
0.366
0.308
0.01
0.09
0.032
0.031
-0.013
0.001
0.104
0.068
-0.03
0.036
0.001
0.035
0.07
0.101
0.061
0.025
0.127
-0.003
-0.013
-0.018
-0.004
-0.005
0.989
0.005
0.005
-0.007
0.999
0.276
0.29
0.277
1.284
0.285
0.286
0.299
1.293
0.309
0.295
0.309
0.296
0.455
0.229
0.426
0.475
0.381
0.184
0.302
0.238
0.011
0.079
0.015
International Electrical Engineering Journal (IEEJ)
Vol. 7 (2017) No.10, pp. 2403-2414
ISSN 2078-2365
http://www.ieejournal.com/
2411 Kheirollahi et. al., Genetic Algorithm Based Optimal Coordination of Overcurrent Relays Using a Novel Objective Function
∆t 16-9
∆t 40-16
∆t 18-16
∆t 37-16
∆t 15-17
∆t 37-17
∆t 40-17
∆t 15-39
∆t 18-39
∆t 37-39
∆t 15-38
∆t 40-38
∆t 18-38
∆t 19-21
∆t 22-20
∆t 17-19
∆t 20-18
∆t 29-22
∆t 24-22
∆t 32-22
∆t 21-23
∆t 29-23
∆t 32-23
∆t 21-30
∆t 24-30
∆t 32-30
∆t 21-31
∆t 24-31
∆t 29-31
∆t 26-27
∆t 23-27
∆t 28-25
∆t 23-25
∆t 26-24
∆t 28-24
∆t 35-37
∆t 38-36
∆t 33-35
∆t 39-35
∆t 36-34
∆t 39-34
∆t 36-40
∆t 33-40
∆t 34-32
∆t 31-33
-0.035
0.11
-0.139
0.515
-0.115
0.431
0.025
-0.051
-0.159
0.496
0.066
0.207
-0.042
-0.138
-0.246
0.052
-0.269
0.011
-0.117
-0.048
-0.156
-0.031
-0.089
0.005
0.002
0.072
-0.054
-0.057
0.071
0.244
-0.115
-0.006
-0.222
0.078
-0.065
-0.053
0.036
-0.078
0.078
-0.011
-0.007
0.092
-0.06
-0.069
-0.121
0.004
0.27
0.006
0.278
0.027
0.137
0.129
0.198
0.037
0.308
0.3
0.402
0.139
0.033
0.02
0.008
0.003
0.066
0.01
0.016
-0.001
0.061
0.011
0.663
0.669
0.675
0.285
0.291
0.347
0.305
0.025
0.374
0.158
0.074
0.008
0.104
0.32
0.011
0.269
0.021
0.003
0.288
0.012
0.028
0.373
0.038
0.137
0.006
0.278
0.002
0.166
0.026
0.144
0.037
0.308
0.39
0.414
0.283
0.04
0.02
0.04
0.003
0.066
0.01
0.016
0.036
0.238
0.189
0.522
0.669
0.675
0.336
0.482
0.538
0.785
0.333
0.431
0.001
0.029
0.008
0.026
0.029
0.061
0.319
0.021
0.003
0.327
0.051
0.028
0.021
0.003
0.064
0.011
0.337
-0.019
0.255
-0.018
0.066
0.013
0.339
0.31
0.311
0.257
0.008
-0.017
-0.021
-0.004
0.024
0.003
0.006
-0.029
0.169
0.151
0.428
0.602
0.608
0.274
0.447
0.471
0.696
0.297
0.399
-0.007
-0.006
0.001
-0.014
0.012
-0.008
0.296
-0.027
0.011
0.262
-0.005
-0.024
0.009
-0.035
0.11
-0.139
0.515
-0.115
0.431
0.025
-0.051
-0.159
0.496
0.066
0.207
-0.042
-0.138
-0.246
0.052
-0.269
0.011
-0.117
-0.048
-0.156
-0.031
-0.089
0.005
0.002
0.072
-0.054
-0.057
0.071
0.244
-0.115
-0.006
-0.222
0.078
-0.065
-0.053
0.036
-0.078
0.078
-0.011
-0.007
0.092
-0.06
-0.069
-0.121
0.038
0.137
0.006
0.278
0.027
0.137
-0.003
0.198
0.037
0.308
0.329
0.299
0.168
0.033
0.02
0.008
0.003
0.066
0.01
0.016
0.029
0.09
0.041
0.663
0.669
0.675
0.285
0.291
0.347
0.287
0.015
0.403
0.151
0.029
0.008
0.104
0.262
0.011
0.269
0.021
0.003
0.327
0.051
0.028
0.373
0.038
0.137
0.006
0.278
0.002
0.166
0.026
0.144
0.037
0.308
0.39
0.414
0.283
0.04
0.02
0.04
0.003
0.066
0.01
0.016
0.036
0.238
0.189
0.522
0.669
0.675
0.336
0.482
0.538
0.785
0.333
0.431
0.001
0.029
0.008
0.026
0.029
0.061
0.319
0.021
0.003
0.327
0.051
0.028
0.021
-0.015
0.094
-0.014
0.367
-0.019
0.255
-0.018
0.097
-0.01
0.371
0.31
0.311
0.203
0.008
-0.019
-0.021
-0.012
0.052
-0.038
-0.033
-0.029
0.169
0.084
0.428
0.536
0.541
0.274
0.381
0.471
0.607
0.297
0.338
-0.007
-0.041
-0.006
-0.014
0.012
-0.008
0.247
0.001
-0.01
0.262
-0.005
-0.029
0.009
Δtmbk < -0.05 Yes No No No Yes No No No
APPENDIXES
Appendix A
P/B relays and the close-in fault currents for IEEE 8-busbars system.
No. of P
Relay
Current
(A)
No. of B
Relay
Current
(A)
1 3230 6 3230
International Electrical Engineering Journal (IEEJ)
Vol. 7 (2017) No.10, pp. 2403-2414
ISSN 2078-2365
http://www.ieejournal.com/
2412 Kheirollahi et. al., Genetic Algorithm Based Optimal Coordination of Overcurrent Relays Using a Novel Objective Function
8 6080 9 1160
8 6080 7 1880
2 5910 1 993
9 2480 10 2480
2 5910 7 1880
3 3550 2 3550
10 3880 11 2340
6 6100 5 1200
6 6100 14 1870
13 2980 8 2980
14 5190 9 1160
7 5210 5 1200
14 5190 1 993
4 3780 3 2240
11 3700 12 3700
5 2400 4 2400
12 5890 13 985
12 5890 14 1870
Appendix B
P/B Relays and the Close-in Fault Currents for IEEE 14-Busbars System.
No. of P Relay Current(
A) No. of B Relay
Current(
A) No. of P Relay
Current(
A) No. of B Relay
Current(
A)
1 11650 6 654 26 4640 30 179
5 12400 2 1980 10 3110 13 1140
2 4260 4 750 10 3110 7 1290
2 4260 12 875 10 3110 25 495
2 4260 8 723 10 3110 30 190
3 7310 1 3920 14 4030 9 2090
3 7310 12 848 14 4030 7 1270
3 7310 8 689 14 4030 25 489
11 7180 4 725 14 4030 30 188
11 7180 1 3920 8 3880 9 2090
11 7180 8 695 8 3880 25 489
7 7330 1 3920 8 3880 13 1120
7 7330 4 716 8 3880 30 188
7 7330 12 845 29 4720 7 1220
13 3280 11 1380 29 4720 9 1990
12 3130 14 1250 29 4720 13 1070
26 4640 13 1120 29 4720 25 449
26 4640 9 2080 6 3830 3 1280
26 4640 7 1270 6 3830 10 1990
6 3830 16 560 32 547 34 547
4 3920 5 1370 33 783 31 783
4 3920 16 562 22 1930 29 499
4 3920 10 1990 22 1930 24 1160
15 4610 5 1360 22 1930 32 280
15 4610 3 1280 23 1200 21 434
International Electrical Engineering Journal (IEEJ)
Vol. 7 (2017) No.10, pp. 2403-2414
ISSN 2078-2365
http://www.ieejournal.com/
2413 Kheirollahi et. al., Genetic Algorithm Based Optimal Coordination of Overcurrent Relays Using a Novel Objective Function
15 4610 10 1970 23 1200 29 499
9 3260 5 1390 23 1200 32 281
37 572 35 572 30 1810 21 424
36 781 38 781 30 1810 24 1130
35 1480 33 368 30 1810 32 275
35 1480 39 1110 27 1430 28 633
34 1390 36 284 25 1430 23 806
34 1390 39 1110 24 1870 26 1230
40 654 36 285 24 1870 28 634
40 654 33 370 18 725 20 725
31 2060 21 428 9 3260 3 1310
31 2060 24 1150 9 3260 16 569
31 2060 29 494 9 3260 16 569
27 2030 23 808 16 1490 40 201
16 1490 18 388 39 2400 37 47
16 1490 37 51 38 2530 15 1110
17 2210 15 1110 38 2530 40 191
17 2210 37 51 38 2530 18 386
17 2210 40 199 21 564 19 564
39 2400 15 1120 20 1310 22 1310
39 2400 18 389 19 955 17 955
International Electrical Engineering Journal (IEEJ)
Vol. 7 (2017) No.10, pp. 2403-2414
ISSN 2078-2365
http://www.ieejournal.com/
2414 Kheirollahi et. al., Genetic Algorithm Based Optimal Coordination of Overcurrent Relays Using a Novel Objective Function
REFERENCES
[1] Vivekananthan J, Karthick R. Voltage Stability Improvement and
Reduce Power System Losses by Bacterial Foraging Optimization
Based Location of Facts Devices. IEEJ 2013; 4: 1034-1040.
[2] Shih M. Y, Enriquez A. C, Trevino L. M. T . On-Line Coordination
of Directional Overcurrent Relays: Performance Evaluation
among Optimization Algorithms. ELECTR POW SYST RES
2014; 110: 122-132.
[3] Ralhan S, Ray S. Directional Overcurrent Relays Coordination
using Linear Programming Intervals: A Comparative Analysis.
India Conference (INDICON), 2013 Annual IEEE; India; 13-15
Dec: pp. 1 - 6.
[4] Ojaghi M, Sudi Z, Faiz J. Implementation of Full Adaptive
Technique to Optimal Coordination of Overcurrent Relays. IEEE
Trans. Power Del 2013; 28: 235-244.
[5] Kargar H. K, Abyaneh H. A, Ohis V, Meshkin M. Pre-Processing of
the Optimal Coordination of Overcurrent Relays. ELECTR POW
SYST RES 2005; 75: 134-141.
[6] Birla D, Maheshwari R. P, Gupta H. O. T ime-Overcurrent Relay
Coordination: A Review. IJEEPS 2005; 2.
[7] Abyaneh H. A, Al-Dabbagh M, Kargar H. K, Sadeghi S. H. H,
Khan R. A. J. A New Optimal Approach for Coordination of
Overcurrent Relays in Interconnected Power Systems. IEEE
Trans. Power Del 2003; 18: 430-435.
[8] Abyaneh H. A, Keyhani R. Optimal Coordination of Overcurrent
Relays in Power System by Dual Simplex Method. AUPEC 1995
Conference, Australia; 3: pp. 440-445.
[9] SO C.W, Li K. K, Lai K. T , Fung K. Y. Application of Genetic
Algorithm for Overcurrent Relay Coordination. Proc. IEEE 1997
Conference in Developments in Power System Protection; pp.
66-69.
[10] Papaspiliotopoulos V, Korres G, and Maratos N, "A novel
quadratically constrained quadratic programming method for
optimal coordination of directional overcurrent relays," 2015 .
[11] A. A. Kida and L. A. G. Pareja" ,Optimal Coordination of
Overcurrent Relays Using Mixed Integer Linear Programming,"
IEEE Latin America Transactions, vol. 14, pp. 1289-1295, 2016.
[12] Urdaneta A.J, Nadira R, Perez L.G. Optimal coordination of
directional over-current relays in interconnected power systems.
IEEE Trans. Power Del 1988; 903–911.
[13] Urdaneta A.J, Restrepo H, Marquez S, Sanchez J. Coordinat ion of
directional overcurrent relay timing using linear programming,
IEEE Trans. Power Del 1996; 122–129.
[14] Chattopadhyay B, Sachdev M.S, Sidhu T .S. An on-line relay
coordinationalgorithm for adaptive protection using linear
programming technique. IEEE Trans. Power Del 1996; 165–173.
[15] Mansour M.M, Mekhamer S.F, El-Kharbawe N.E.-S. A modified
particle swarm optimizer for the coordination of directional
overcurrent relays, IEEE Trans. Power Del 2007; 1400–1410.
[16] Mohammadi R, Abyaneh H.A, Razavi F, Al-Dabbagh M, Sadeghi
S.H.H. Optimal relays coordination efficient method in
interconnected power systems. JInt J Elec Eng 2010; 61(2):75-83.
[17] Singh M, Panigrahi B.K. Optimal overcurrent relay coordination
in distribution system, in: International Conference Energy,
Automation, and Signal (ICEAS) 2011; 1–6.
[18] Singh D.K, Gupta S. Optimal coordination of directional
overcurrent relays: agenetic algorithm approach, in: IEEE
Students’ Confe. on Electrical, Elec-tronics and Computer Science;
2012.
[19] V. Kale, M. Agarwal, P. D. Kesarkar, D. R. Regmi, A. Chaudhary,
and C. Killawala, "Optimal coordination of overcurrent relays
using genetic algorithm and simulated annealing," in Control,
Instrumentation, Energy and Communication (CIEC), 2014
International Conference on , pp. 361-365, 2014.
[20] J. M. Ghogare and V. Bapat, "Field based case studies on optimal
coordination of overcurrent relays using Genetic Algorithm," in
Electrical, Computer and Communication Technologies
(ICECCT), 2015 IEEE International Conference on , pp. 1-7,
2015.
[21] Uthitsunthorn D, Kulworawanichpong T . Optimal overcurrent
relay coordination using genetic algorithms, in: International
Conf. on Advances in Energy Engineering 2010.
[22] Noghabi A.S, Sadeh J, Mashhadi H.R. Considering different
network topologiesin optimal overcurrent relay coordination
using a hybrid GA, IEEE Trans. Power Del 2009; 1857–1863.
[23] Motie Girjandi A, Pourfallah M. Optimal coordination of
overcurrent relays by mixed genetic and particle swarm
optimization algorithm and comparison of both, in: International
Conf. on Signal, Image Processing and Applica-tions 2011.
[24] Kheirollahi R, Namdari F. Optimal Coordination of Overcurrent
Relays Based on Modified Bat Optimization Algorithm. IEEJ
2014; 5: 1273-1279.
[25] Mahari A, Seyedi H, An analytic approach for optimal
coordination of overcurrent relays. IET GENER TRANSM DIS
2013; 7: 674 -680.
[26] C. W. SO, K. K. Li. Overcurrent Relay Coordination by
Evolutionary Programming. ELECTR POW SYST RES 2000; 53:
83-90.
[27] SO C. W, Li K. K. T ime Coordination Method for Power Syst em
Protection by Evolutionary Algorithm. IEEE Trans. Ind. Appl
2000; 36: 1235-1240.
[28] SO C. W, Li K. K. Intelligent Method for Protection
Coordination. IEEE 2004 International Conference of Electric
Utility Deregulation Restructuring and Power Technology; 5-8
April 2004; IEEE pp. 378-382.
[29] Zeineldin H, EL-Saadany E. F, Salama M. A. Optimal
Coordination of Directional Overcurrent Relay Coordination.
IEEE POWER ENG SOC 2005; 2: 1101-1106.
[30] M. Thakur and A. Kumar, "Optimal coordination of directional
over current relays using a modified real coded genetic algorithm:
A comparative study," International Journal of Electrical Power
& Energy Systems, vol. 82, pp. 484-495, 2016.
[31] Razavi F, Abyaneh H. A, Al-Dabbagh M, Mohammadi R,
Torkaman H. A New Comprehensive Genetic Algorithm Method
for Optimal Overcurrent Relays Coordination. IEEE Trans.
Power Del 2008; 78: 713-720.
[32] Prachi R, Shinde, Madhura Gad. Genetic Algorithm Approach into
Relay Coordination. IJEET 2013; 4:35-42.
[33] Arabali A, Ghofrani M, Etezadi-Amoli M, Fadali M. S, Baghzouz Y.
Genetic-Algorithm-Based Optimization Approach for Energy
Management. IEEE Trans. Power Del 2013; 28: 162-170.
[34] Bedekar P. P, Bhide S. R. Optimal Coordination of Directional
Overcurrent Relay Using Hybrid GA-NLP Approach. IEEE
Trans. Power Del 2011; 26: 109-119.
[35] Kamel S, Kodsi M. Modeling and Simulation of IEEE 14 bus
System with Facts Controllers 2009.