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

[email protected]


mailto:[email protected]


Vol. 7 (2017) No.10, pp. 2403-2414

ISSN 2078-2365



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



Vol. 7 (2017) No.10, pp. 2403-2414

ISSN 2078-2365



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.



Vol. 7 (2017) No.10, pp. 2403-2414

ISSN 2078-2365



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.



Vol. 7 (2017) No.10, pp. 2403-2414

ISSN 2078-2365



*

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



Vol. 7 (2017) No.10, pp. 2403-2414

ISSN 2078-2365



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



Vol. 7 (2017) No.10, pp. 2403-2414

ISSN 2078-2365



∆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



Vol. 7 (2017) No.10, pp. 2403-2414

ISSN 2078-2365



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



Vol. 7 (2017) No.10, pp. 2403-2414

ISSN 2078-2365



∆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



Vol. 7 (2017) No.10, pp. 2403-2414

ISSN 2078-2365



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



Vol. 7 (2017) No.10, pp. 2403-2414

ISSN 2078-2365



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



Vol. 7 (2017) No.10, pp. 2403-2414

ISSN 2078-2365



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