Modified water cycle algorithm for optimal direction overcurrent relays coordination

Accepted Manuscript Modified water cycle algorithm for optimal direction overcurrent relays coordination Ahmed Korashy, Salah Kamel, Abdel-Raheem Youssef, Francisco Jurado

PII: DOI: Reference:

S1568-4946(18)30577-5 https://doi.org/10.1016/j.asoc.2018.10.020 ASOC 5138

To appear in:

Applied Soft Computing Journal

Received date : 12 April 2018 Revised date : 20 September 2018 Accepted date : 10 October 2018 Please cite this article as: A. Korashy, et al., Modified water cycle algorithm for optimal direction overcurrent relays coordination, Applied Soft Computing Journal (2018), https://doi.org/10.1016/j.asoc.2018.10.020 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

*Highlights (for review)

Highlights

Optimization model of directional over current relays coordination. Modified version for Water Cycle Algorithm. The main objective is to minimize the operating times of all relays. Time dial setting and pickup current setting or plug setting. Balance between explorative and exploitative phases.

Graphical abstract (for review)

Graphical abstract

Time dial setting

Network data such as (fault currents, current transformer ratio, relay pairs)

Goal function (Min. Σ operating time of primary relays)

Decision Variables (time dial setting & pick up current)

Direction over current relays

Modified Water Cycle Algorithm

DigSILENT PowerFactory is used for verifying the proposed algorithm

Pickup current

Graphical abstract for solving DOCRs coordination problem using modified water cycle algorithm

*Manuscript Click here to view linked References

Modified Water Cycle Algorithm for Optimal Direction Overcurrent Relays Coordination Ahmed Korashy1,2, Salah Kamel1,3, Abdel-Raheem Youssef4, Francisco Jurado2, 1

Electrical Engineering Department, Faculty of Engineering, Aswan University, 81542 Aswan, Egypt 2 Department of Electrical Engineering, University of Jaén, 23700 EPS Linares, Jaén, Spain 3 State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University, Chongqing, China 4 Electrical Engineering Department, Faculty of Engineering, South Valley University, Qena, Egypt

Abstract: The optimization model of Directional Over Current Relays (DOCRs) coordination is considered non-linear optimization problem with a large number of operating constraints. This paper proposes a modified version for Water Cycle Algorithm (WCA), referred to as MWCA to effectively solve the optimal coordination problem of DOCRs. The main goal is to minimize the summation of operating times of all relays when they act as primary protective devices. The operating time of a relay depends on time dial setting and pickupcurrent setting or plug setting, which they are considered as decision variables. In the proposed technique, the search space has been reduced by increasing the C-value of traditional WCA, which effects on the balance between explorative and exploitative phases, gradually during the iterative process in order to find the global minimum. The performance of proposed algorithm is assessed using standard test systems; 8-bus, 9-bus, 15-bus, and 30-bus. The obtained results by the proposed algorithm are compared with those obtained by other well-known optimization techniques. In addition, the proposed algorithm has been validated using benchmark DIgSILENT PowerFactory. The results show the effectiveness and superiority of the proposed algorithm to solve DOCRs coordination problem, compared with traditional WCA and other optimization techniques. Keywords: Direction overcurrent relays; Coordination time interval; Optimal coordination; Modified Water cycle algorithm.



Corresponding author: Tel.: +34 953 648518; Fax: +34 953 648586. E-mail addresses: [email protected] (F. Jurado), [email protected](S. Kamel),[email protected] (A. Youssef),[email protected](A. Korashy)

1

1. Introduction The complexity of power system operation is continually increased due to its extension with years. Protection relaying plays an important role in power systems. It is mainly intended to detect and identify the faulted parts as fast as possible for keeping safe the system and people [1]. Basically, Over Current Relay (OCR) is a type of protective relays that operates when the current exceeds a predetermined value. The combination of the directional unit with each OCR is called DOCRs [2]. DOCRs may compare the phase angle of a current with a voltage, or the phase angle of a current with another current to determine the direction to a fault [3]. DOCRs operate only when the current magnitude exceeds a present value and flows in the same direction as DOCR [4]. The DOCRs have two settings, Time dial setting (TDS) and Pickup current setting (Ip) or Plug Setting (PS). The operating time of a relay depends on these settings. Appropriate coordination between the protection relays is a very important issue to maintain the reliability of the overall protection system. The optimal coordination of DOCRs aims to find suitable relay settings and keep a coordination time margin between primary and backup relays [5]. In other words, the backup relay should operate in case of the primary relay fails to take the appropriate action [6]. In literature, many algorithms have been proposed to solve the coordination problem and find the optimal relay settings. At the first, before the involvement of computers, the calculation of relay settings was done manually. This calculation was inappropriate practically and very time consuming [7]. In the year 1960s, the trial-and-error approach was initiated using computers to find the optimal relay setting [8]. This approach has a slow rate of convergence and the obtained TDS values of the relays are relatively high. In the late eighties, the coordination problem of DOCRs was solved by the Linear Programming (LP) method [9]. In this approach, TDS is calculated via LP for a fixed value of

. In contrast, LP is a simple and

fast approach, but it is needed an expert for setting the initial value of

2

and may get stuck

in local minima. Nonlinear programming (NLP) has been used in order to optimize both relay settings and solve the relay coordination problem [10]. Although NLP gives better results, it very complex and may be trapped in local minima with wrong initial values of

and TDS

[8]. Recently, meta-heuristic optimization algorithms became suitable tools to solve the nonlinear coordination problem. Different algorithms have been proposed to solve the coordination problem of DOCRs such as: -Particle Swarm Optimization (PSO) that was inspired by the social and cooperative behavior of birds in navigating and hunting to fill their needs in the search space [11-14]. -Genetic algorithm (GA) that simulates Darwinian evolution concepts [13-15]. GA starts with a random population called chromosomes. After evaluating the candidate solution by the objective function, it modifies the variables of solutions based on their fitness value and the new population is formed. The entire process is repeated and endeavours to reach the optimal solution by cross over, mutation, and reproduction operations [14-16]. Initialization with a random population is the main similarity between GA and PSO. PSO has the ability to keep track of the position, but unlike PSO, GA can only keep information regarding the position of the members of the population [15]. Also, PSO doesn’t survival of the fittest but it mainly depends on “constructive co-operation” among the individuals (agents) [15]. - Ant colony optimization (ACO) that simulates ant’s behaviour in finding the shortest path between their home colony and a source of food [16, 17]. -Harmony search algorithm (HS) that based on the creative process of music composition of searching for a perfect state of harmony [7, 12]. - Seeker algorithm that based on the behaviour of human memory uncertainty reasoning, consideration, experience gained, and social learning [6].

3

Other optimization algorithms have been proposed to solve the coordination problems of DOCRs such as; Firefly algorithm (FFA) [1], Black Hole (BH) [18], Electromagnetic Field Optimization (EFO) [19], Modified Electromagnetic Field Optimization (MEFO) [20], Biogeography-based optimization (BBO) [8], and Gravitational Search Algorithm (GSA) [21]. Recently, hybrid methods have been proposed to solve the coordination of DPCRs problem, which collects the features of classical and nature inspired methods such as; Cuckoo Search Algorithm (CSA)-FFA [22], GA-NLP [23], BBO-Differential Evaluation (DE) [24], and BBO-LP [4]. WCA is a metaheuristic algorithm that inspired by the hydrological cycle in nature. MCA starts with an initial population of candidate solution called raindrops, which given for each test case. The design variables (TDS and Ip) are represented by raindrops. The ranges of TDS and Ip are given for each test case. Each raindrop is evaluated according to the main objective function, then it is classified as stream, river, or sea. This process is repeated until the convergence criteria is met and the optimal relay setting subject to the operating constraints (TDS, Ip, CTI) is obtained. The main contributions of this paper can be summarized as follows: - An effective optimization algorithm, called modified Water Cycle Algorithm (MWCA) has been proposed to solve the optimal coordination problem of DOCRs; -MWCA optimization algorithm has been proposed to improve the performance of the original WCA; - In the proposed algorithm, the search space has been reduced by increasing the C-value of traditional WCA, which effects on the balance between explorative and exploitative phases, gradually during the iterative process in order to find the global minimum;

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- The performance of the proposed algorithm has been assessed using different standard test systems (8-bus,9-bus, 15-bus, and 30-bus); - The results obtained by the proposed algorithm has been validated using benchmark DIgSILENT PowerFactory; - Using the proposed algorithm, remarkable minimization in total operating time of all primary relays subject to the sequential operation between relay pairs has been achieved; - The proposed algorithm has been compared with different well-known optimization algorithms; - The obtained results prove the effectiveness and superiority of the proposed MWCA to solve the DOCRs coordination problem, compared with traditional WCA and other optimization techniques; - The proposed optimization algorithm can be used to effectively solve other optimization problems. The rest of the paper is organized as follows: Section 2 presents the problem formulation of DOCRs coordination. Section 3 presents the traditional WCA and the proposed MWCA. In Section 4, the simulations carried out and the most relevant results obtained are reported. Finally, the main conclusions are duly drawn in Section 5. 2. Problem Formulation 2.1 Objective function The study of optimal DOCRs coordination aims to find the optimal relay settings in order to protect the system, where, the primary relays are operated in the first to clear the faults, then the corresponding backup relays should be operated in case of failing the primary relays. This process is achieved according to coordinated time and satisfying the other operating constraints. The DOCRs coordination can be formulated as a constrained optimization

5

problem. The objective function is to minimize the sum of operating times for all primary relays. The objective function can be described as follows:

(1) The operating time for each protective relay is defined as:

(2) (3) where α, β and γ are constant values given by 0.14, 0.02 and 1.0 respectively.

is the

operating time of relay. N is the number of primary relays in the system. If is the fault current (A), and CT is the current transformer ratio [5, 25]. 2.2 Operating constraints The object function is subjected to the following operating constraints: 2.2.1 Relay characteristics constrain Limits of relay settings can be expressed as: (4) (5) (6)

and

are the lower and upper pickup current, respectively.

and

are

the lower and upper plug setting, respectively.

and

are the minimum and the

maximum value of TDS, respectively. The range of

is based on the minimum fault current

and the maximum load current seen by the relay. The range of TDSis based on the relay manufacturer [8]. 2.2.2 Coordination constraints

6

The second type of operating constraints is the coordination constraints. The coordination time interval (CTI) between primary and backup relays can be written as: (7) where,

and

are the operating times of backup and primary relays,

respectively. The value of CTI varies from 0.30 to 0.40 seconds for electromechanical relays while it varies from 0.10 to 0.20 (s) for numerical relays [5,22]. The penalty function is used to handle the coordination constraints. A penalty term is added to the objective function in order to penalize the unfeasible solutions. A comprehensive survey of the most popular penalty functions is given in [26]. 3. Water Cycle Algorithm WCA is inspired from nature and based on the observation of the water cycle process. In the water cycle, evaporated water is carried into the atmosphere and back to the earth in the form of rain [27]. 3.1. Mathematical Modeling WCA can be mathematically modelled as follows: 3.1.1 Initialization of Raindrops WCA begins with initial raindrops, which is randomly initiated between lower and upper boundaries as given (4), (5), and (6). The best raindrop that has the minimum objective function is chosen as a sea and the good raindrops are chosen as a river [27]. Then, the rest of the raindrops are chosen as streams. The population is generated randomly over the search space as:

(8)

7

(9) where, Nvars is number of decision variables, and Npop is number of raindrops. Depending on the value of the object function, the cost of a raindrop is evaluated as:

(10) The raindrops which have the minimum values are chosen as sea and rivers. The summation of a number of rivers and the single sea is given in (11). The rest of the raindrops form the streams can be calculated using (12). (11) (12) In order to compute the raindrops that designated to the rivers and sea depending on the flow intensity as:

(13) 3.1.2 A stream flow to the rivers or sea Streams flow to rivers or directly flow to the sea. Also, rivers flow to the sea. The new position for streams and rivers may be given as:

(14) (15)

8

where C is a value between 1 and 2, X stream is position of streams, and X river is position of river, and X sea is position of sea [27]. The value of rand is random number between 0 and 1. The position of a stream should be exchanged with river position if a stream explores a better solution compared to the river. Same exchange can happen for rivers and the sea [27]. 3.1.3 Evaporation condition The evaporation process is a very important stage that can prevent the algorithm from trapped in local minima. The evaporation condition is applied to both rivers and streams that flow into the sea [27]. Following pseudocode is used to check the evaporation condition [28]:

Pseudocode1: Start raining process End where,

is a small value.

The evaporation process is applied when the distance between a river and sea is less than

, which indicate that the river has reached the sea, then, the raining process will be

applied. Also, the evaporation condition is used to check the streams belong to the sea. Following pseudocode explains that [27]:

Pseudocode2: Start raining process End The value of

is decreased as follows:

(16) 3.1.4 Raining process

9

The raining process is started after satisfying the evaporation condition. The new raindrops form streams in the different locations. The new locations of the newly formed streamscan be calculated as follows: (17) where, LB and UB are lower and upper ranges of decision variables, respectively. In the case of a constrained problem, the new locations of the newly formed streams which directly flow to the sea can be calculated as follows: (18) where is a small value that leads the algorithm to search in the smaller region near the sea. The best value for

may be chosen as 0.1 [28].

3.2. Modified Water Cycle Algorithm It is well known that the performance of all population-based algorithms can be enhanced by balancing the capability of exploitation and exploration in order to find the global optimal solution and reduce the search space [29]. Exploration and exploitation phases are two conflicting milestones and both are necessary for population-based algorithms. A proper balance between exploration and exploitation can guarantee the global minima. The exploitation phase aims for searching locally around the promising solutions, while exploration phase has the ability for search into the solutions space [30-31]. In WCA algorithm [28], the balance among exploration and exploitation phases can be achieved according to the value of parameter C. The C-value enables the streams to flow in different directions towards the rivers when it is being greater than one [28]. The C-value is chosen as 2 in the traditional WCA algorithm [28, 32]. In the proposed MWCA, we suggest to increase the C-value gradually from 1 to 2 according to (19). This modification improves the balancing between exploration and exploitation phases to search for the global optimal solution by increasing the C-value exponential over the course of iterations instead of being

10

chosen as a constant value. Consequently, the computation time of the proposed MWCA is reduced compared with the original WCA. The new position of streams and rivers can be calculated as follows:

(19) (20) (21)

The raining process for all newly formed streams can be calculated using (18) to improve searching for the global minimum in the whole space. In traditional WCA, Eq. (18) used only for streams which flow directly to the sea [26]. The following pseudocode is used to check the evaporation condition for rivers flows to sea:

Pseudocode 3: Start raining process using (18) End The pseudocode that used to check the evaporation condition for streams flow directly to the sea:

Pseudocode 4: Start raining process using (18) End The overall solution process of DOCRs coordination problem using the proposed MWCA can be summarized in the following flowchart shown in Fig. 1:

11

Start Fault currents, primary and backup pairs, lower and upper limits of decision variables, CT ratio

Read the netwok input data

Input population size, number of decision variables, Max. Iteration, dmax& Nsr

Input MWCA algorithm data

Raindrop = x1 , x2 , x3 ,

, xNvar

Initialize population and form the initial streams, rivers, and sea using (8), (11), and (12), respectively

Nsr = Number of Rivers + 1

NRaindrops = Npop

Nsr

N

OF =

Evaluate the object function for each raindrops using (1)

Ti i=1

Set current iteration i=1

NSn = round

i = 𝐂 𝐢 C= 𝟐2

Cost n

× NRaindrops Cost i = 1,2, . Nsr

N sr i=1

𝟏1

2 i𝐢 Max. ilteration 𝐌𝐚𝐱. 𝐢𝐥𝐭𝐞𝐫𝐚𝐭𝐢𝐨𝐧

,

Calculate the intensity of flow for sea and river using (13)

𝟐

Calculate the C- value using (19)

i+1 i X Stream = X Stream + rand × C i × X iRiver X iStream

Streams flow to the river using (20)

i+1 i X River = X River + rand × C i i i × X Sea X River

River flow to sea using (21)

NO

Is the solution given by stream better than the solution given by river ?

i  i 1

Yes

Exchange the positions of the stream with this river

Is the solution given by river better than the solution given by sea ?

NO

Yes Exchange the positions of the river with this sea

NO

Check the evaporation condition using Pseudo-code 3and Pseudo-code 4

Yes Start raining process using (18)

Calculate the value of dmax using (16)

Maximum number of Iteration = 500

Check the convergence criteria

i di+1 max = dmax

dimax Max. Ilteration.

new XStream = Xsea + µ×randn 1,Nvar

NO

Yes Relay Setings (TDS& Ip) for each Relay

Print the optimal values

End

Fig. 1. Solution process of DOCRs coordination problem using the proposed MWCA

12

4. Results and Discussions The proposed algorithm has been tested using four standard test systems (8-bus, 9-bus, 15bus, and IEEE-30 bus) and compared with traditional WCA and other well-known optimization algorithms (FFA [1], SOA [6], HS [7], BBO [8], GA [15], BH [18], EFO [19], MEFO [20], GSA [21], GA-NLP [23], BSA [33] and GSA-SQP [34]). The control parameters of the MWCA algorithm such as dmax is equal to10 e-5, and Nsr is equal to 10, and the number of raindrops is equal to 50 for all test cases. The proposed algorithm is carried out in MATLAB environment using a 2.3 GHz PC with 4 GB RAM under Windows 7 operating systems. 4.1. Case1: 8-bus test system In this case, the proposed MWCA is validated using 8-bus test system. The single line diagram of this system is shown in Fig. 2. This system consists of 7 lines and 14 relays, 2 transformers and 2 generators. The

and

limits are 0.05 and 1.1, respectively.

The CTI is set to 0.3 s. The details of this system such as; Ip ranges, fault currents, the primary and backup relationship of relay pairs can be found in [5, 35]. The optimal values of TDS and

using MWCA is presented in Table 1. The operating time

of primary and backup relays and CTI values are tabulated in Table 2 and represented graphically in Fig. 3. From Table 1 and Table 2, it can be observed that the MWCA satisfies all the operating constraints of relay settings and minimize the total operating time of the relays.

13

G1

Bus 7

T1 Bus 1

Bus 3 8

1 Bus 2

14

9

2

13

6

Bus 4 10

3

7

4

5

12

11

Bus 5

Bus 6 T2

Bus 8 G2

Fig. 2. Single line diagram of 8-bus test system Table 1 Optimal relay setting of the 8-bus test system Relay No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 𝐢 𝟏 𝐢 (s)

Ip 480 396.2657 315.4322 314.713 273.8567 120 319.9939 217.695 272.6356 479.9938 292.7829 480 480 320 6.4

TDS 0.074154 0.26745 0.19345 0.108356 0.05 0.273101 0.227087 0.216191 0.05 0.079703 0.195723 0.242363 0.073249 0.224022

14

Primary Relay

1.2

Backup Relay

Operting Time (s)

1 0.8 0.6 0.4 0.2 0 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Primary - Backup Relay Pair

Fig. 3 Operating times of primary and backup relaysof 8-bus system Table 2 Primary and backup operating time of relays and CTI values of the 8-bus system Relay pairs 1 2 3 4 5 6 6 7 7 8 8 9 10 11 12 12 13 14 14

6 1 2 3 4 5 5 5 13 7 9 10 11 12 13 14 8 1 9

𝐫𝐢 𝐚𝐫 (s) 0.29757 0.69945 0.69945 0.561462 0.380977 0.21754 0.494373 0.494373 0.59898 0.598985 0.468715 0.468715 0.208525 0.349194 0.540261 0.685352 0.685352 0.307456 0.59097

(s) 𝐚 0.59757 0.99945 0.99945 0.861462 0.680977 0.51754 0.898987 0.985352 0.89898 0.985352 0.999458 0.890971 0.508525 0.649194 0.840261 0.985352 0.985352 0.607458 0.999458

𝐂 0.3 0.3 0.3 0.3 0.3 0.3 0.404614 0.49098 0.3 0.386367 0.530743 0.422256 0.3 0.3 0.3 0.3 0.3 0.300002 0.408488

The convergence characteristics of MWCA and traditional WCA are shown in Fig.4. This figure shows that the proposed MWCA algorithm reaches to the final solution faster than the traditional WCA. The best operating time of all primary relays obtained by MWCA is 6.4 s compared with those obtained by WCA, BBO, BH, PSO, DE, EFO, LP, and NLP which equal 8.714 s, 7.54 s, 11.4 s, 10.42 s, 6.65 s, 7.61 s,11.06 s, 6.41s, respectively. The MWCA reaches to the minimum objective function (6.4 s) after computation time about 20 s and 170

15

iterations while the WCA reaches to the minimum objective function (8.714 s) after computation time about 132 s and 2550 iterations. The statistical evaluation of results obtained by different optimization algorithms is presented in Table 3. This table gives the best, the worst, and the mean values of the objective function with its standard deviation obtained by MWCA, EFO, MEFO, BH, BBO, and HS. 40

MWCA

WCA

Objective Function (s)

35 30 25 20 15 10 5

1 89 177 265 353 441 529 617 705 793 881 969 1057 1145 1233 1321 1409 1497 1585 1673 1761 1849 1937 2025 2113 2201 2289 2377 2465 2553 2641 2729 2817 2905 2993

0

Iteration

Fig. 4. Convergence characteristics of MWCA and WCA (8-bus system) From this table, it can be observed that the worst value (6.939 s) of the objective function obtained by MWCA are close to the best value (6.4 s), which indicate the robustness of the MWCA. The standard deviation for the MWCA is lower than EFO, MEFO, and BH, that indicates the high quality of MWCA compared with these algorithms. The objective function for 30 individual runs of the proposed algorithm are calculated and graphically presented in Fig. 5. This figure proves the robustness the proposed algorithm for different runs. Table 3 Statistical analysis of 8-bus system Parameters Mean Standard Deviation Worst Best Number of Runs Violation

MWCA 6.939 0.333 7.55 6.4 30 0

EFO 9.887 0.767 10.867 7.611 30 0

16

BH 12.817 0.844 16.091 11.401 30 0

BBO 8.606 0.584 10.304 10.304 30 0

HS 12.525 0.397 13.301 13.301 30 0

Objective Function (s)

14 12 10 8 6 4 2 0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22

Run Number

Fig. 5. The objective function obtained by MWCA for 30 different runs (8-bus system)

4.2. Case2: 9-bus test system The second test system considered in this section is the 9-bus system. The single line diagram of this system is shown in Fig. 6. This system consists of 12 lines, 24 relays, 48 of primary and backup relay pairs, and 76 optimization variables. The initial ranges for

and

are 0.025 and 1.2, respectively. The Ipmin and Ipmax limits are in [5]. The CT ratio for each relay is 500:1 and the CTI are set to 0.2 s as [5]. More details of this system such as; fault currents and primary, the backup relationship between relay pairs, and load currents can be found in [5].

Bus 7 1

18

16

2 Bus 8

Bus 6 15

20

17

19

Bus 5 13

14

22

12

21

11 Bus 4

Bus 1

10

23

3

G1

4 Bus 2

5

6

24

Bus 6

7

7 Bus 3

Fig. 6. Single line diagram of 9-bus test system.

17

9

The optimal values of TDS and Ip obtained by MWCA are listed in Table 4. The operating time of the primary and backup relays and CTI value are tabulated in Table 5. From Table 4 and Table 5, it can be observed that the MWCA satisfies all the constraints of relay setting and minimize the total operating time of the relays. Table 4 Optimal relay settings of the 9-bus system Relay No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 𝐢 𝟏 𝐢 (s)

Ip 655.7957 362.908 469.6697 444.3489 300.6691 501.8982 520.3822 315.0738 322.5312 499.8417 330.1319 305.3046 355.1842 477.5441 410.416 406.7104 750.2414 909.8112 731.3053 854.0383 726.0842 766.8651 819.5328 708.2386 3.7074

TDS 0.041019 0.032934 0.049491 0.043197 0.049984 0.047344 0.049146 0.047245 0.060409 0.045283 0.036161 0.051961 0.057504 0.046453 0.058828 0.047536 0.027226 0.025004 0.029361 0.025 0.030557 0.025 0.025502 0.025

Table 5 Primary and backup operating time of relays and CTI of 9-bus system Relay pairs 1 1 2 3 4 5 6 6 7 7 8 9 10 11 12

(s) 0.140449 0.140449 0.150898 0.190161 0.167765 0.193393 0.14971 0.14971 0.158106 0.158106 0.187828 0.198022 0.180377 0.155732 0.160222

(s) 0.389535 0.347772 0.350898 0.390161 0.367765 0.393393 0.402911 0.358285 0.40291 0.358285 0.387828 0.398022 0.380391 0.355732 0.360222

𝐫𝐢 𝐚𝐫

15 17 4 1 6 3 8 23 5 23 10 7 12 9 14

𝐚

18

𝐂 0.249086 0.207322 0.2 0.2 0.2 0.2 0.253201 0.208575 0.244804 0.200179 0.200001 0.2 0.200014 0.2 0.2

12 13 13 14 14 15 15 16 16 17 18 18 19 20 20 21 22 22 23 24 24

21 11 21 16 19 13 19 2 17 2 15 13 16 11 14 5 8

0.160222 0.168083 0.168083 0.146786 0.146786 0.173482 0.173482 0.147688 0.147688 0.080362 0.189535 0.189535 0.086578 0.154151 0.154151 0.088908 0.159402 0.159402 0.076948 0.20291 0.20291

0.368087 0.368083 0.368087 0.354151 0.373482 0.373482 0.373482 0.389535 0.347772 0.389535 0.389535 0.373482 0.354151 0.368083 0.360222 0.40291 0.40291

0.207865 0.2 0.200004 0.207365 0.226696 0.2 0.2 0.241847 0.200083 0.2 0.2 0.219331 0.2 0.208681 0.20082 0.2 0.2

The convergence characteristics of MWCA and WCA algorithm are shown in Fig. 7. From this figure, it can be observed that the MWCA algorithm gives better convergence compared to WCA algorithm. The best operating time of all primary relays obtained by MWCA is 3.707 s, while the solution obtained with WCA, GA, PSO, GA-NLP, FFA, MEFO, HAS, and CSA are 7.989 s, 7.494 s, 6.895 s, 4.8015 s, 6.3442 s, 5.225 s, 4.9046 s, and 5.1836 s, respectively. The MWCA reaches to the minimum objective function (3.707 s) after computation time about 70.5 s and 1405 iterations while the WCA reaches to the minimum objective function (7.989 s) after computation time about 79.46 s and 1020 iterations.

19

40

MWCA

WCA

Objective Function (s)

35 30 25 20 15 10 5

1 89 177 265 353 441 529 617 705 793 881 969 1057 1145 1233 1321 1409 1497 1585 1673 1761 1849 1937 2025 2113 2201 2289 2377 2465 2553 2641 2729 2817 2905 2993

0

Iterations

Fig. 7. Convergence characteristics of MWCA and WCA (9-bus system) The statistical evaluation of the results obtained by different optimization techniques is presented in Table 6. This table gives the best, the worst, and the mean values of the objective function along with its standard deviation obtained by MWCA, MEFO, BBO, GA, GA-NLP, FFA, CSA, and HAS. From this table, it can be observed that the best value (3.707 s), the worst value (3.857 s), and the mean value (3.811 s) obtained by MWCA which are the least values compared to the other techniques. This means that the MWCA gives the lowest standard deviation (0.045). The objective function for 30 individual runs of the proposed algorithm are calculated and graphically presented in Fig. 8. This figure proves the robustness the proposed algorithm for different runs. Table 6 Statistical analysis of 9-bus system Parameters Mean Standard Deviation Worst

MWCA 3.811 0.045 3.857

MEFO 6.088 1.223 12.101

BBO 5.634 0.215 6.035

GA 9.4254 1.2643 10.9015

GA-NLP 5.8383 0.9048 6.9982

FFA 7.3282 0.6689 8.1122

CSA 5.4530 0.1964 5.8715

HAS 4.9668 0.0319 5.0223

Best Number of Runs Violation

3.707 30 0

5.225 30 0

5.243 30 0

7.4947 50 0

4.8015 50 0

6.3442 50 0

5.1836 50 0

4.9046 50 0

20

8

Objective Function (s)

7 6 5 4 3 2 1 0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Run Number

Fig. 8. The objective function obtained by MWCA for 30 different runs (9-bus system) 4.3. Case 3: 15-bus test system The 15-bus system is taken as the third test system to validate the proposed algorithm. The single line diagram of this system is shown in Fig. 9. This system consists of 21 lines, 42 relays, 82 coordination constraints, and 84 optimization variables. The

and

limits are 0.1 and 1.1, respectively. The CTI is set to 0.2 s as in [5, 7]. Primary and the backup relationship of relay pairs, Ip ranges, and the fault currents of this system are given in [5,6].

21

DG1

DG2

Bus 1 1

3

Bus 14 7

4

`

2

5

Bus 2 6

Bus 4

8

Bus 5

15

Bus 3

9

11

10

13

12

14

Bus 6

19

23

DG3

DG4

17

`

16

Bus 7

18 Bus 8

20

25

21

Bus 9

22

29

24 33

EG

27 Bus 10

`

26

28 Bus 11

30

32

31

35

41

37

38

`

36

34

Bus 12

40

39

Bus 13

Bus 14

42

Bus 15 DG6

DG5

Fig. 9. Single line diagram of 15-bustest system.

The optimal values of TDS and

obtained by MWCA is listed in Table 7. The operating

time of primary and backup relays and CTI values are tabulated in Table 8. From Table 7 and Table 8, it can be observed that the MWCA satisfies all the constraints of relay setting and minimize the total operating time of the relays.

22

Table 7 Optimal relay settings of the 15-bus system Relay No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 𝐢 𝟏 𝐢 (s)

Ip 280.2922 413.7723 245.8919 332.5621 202.2677 175.0363 157.756 391.6253 173.8936 235.8908 337.095 323.8432 251.0755 394.8639 369.5838 195.8039 101.5643 550.73 224.9802 444.2697 505.1008 135.4993 393.7941 166.8112 195.3116 189.5616 207.2712 238.9244 526.0362 117.366 213.2933 159.3708 167.2435 93.33603 200.7562 245.0295 301.0705 142.6343 115.7605 246.5046 104.2332 273.7499 13.308

TDS 0.1 0.100001 0.125528 0.104592 0.152178 0.132714 0.138179 0.106075 0.135802 0.120768 0.102297 0.107519 0.12659 0.1 0.100072 0.100001 0.118703 0.100012 0.120982 0.1 0.1 0.103831 0.1 0.106319 0.126644 0.109419 0.118916 0.133041 0.10555 0.114982 0.117387 0.125322 0.171734 0.163136 0.126973 0.122209 0.132817 0.138298 0.142472 0.155183 0.176561 0.101101

Table 8 Primary and backup operating time of relays and CTI of 15-bus system Relay pairs 6 1 4 2 16 2 1 3 16 3 7 4

𝐫𝐢 𝐚𝐫 (s) 0.266639 0.283776 0.283776 0.306788 0.306788 0.27669

(s) 𝐚 0.466639 0.483776 0.517938 0.621998 0.517938 0.485918

23

𝐂 0.2 0.2 0.234162 0.31521 0.21115 0.209227

4 4 5 6 6 7 7 8 8 8 9 9 10 11 11 11 12 12 13 14 14 15 15 16 16 17 17 18 18 18 19 19 19 20 20 20 21 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 29 30 30

12 20 2 8 10 5 10 3 12 20 5 8 14 3 7 20 13 24 9 11 24 1 4 18 26 15 26 19 22 30 3 7 12 17 22 30 17 19 30 23 34 11 13 21 34 15 18 28 36 25 36 29 32 17 19 22 27 32

0.27669 0.27669 0.370187 0.332816 0.332816 0.340642 0.340642 0.291566 0.291566 0.291566 0.326639 0.326639 0.302836 0.273087 0.273087 0.273087 0.286376 0.286376 0.331202 0.278007 0.278007 0.268249 0.268249 0.281078 0.281078 0.276756 0.276756 0.249707 0.249707 0.249707 0.285918 0.285918 0.285918 0.238889 0.238889 0.238889 0.242236 0.242236 0.242236 0.265359 0.265359 0.270485 0.270485 0.276457 0.276457 0.351391 0.351391 0.299274 0.299274 0.358061 0.358061 0.385735 0.385735 0.259976 0.259976 0.259976 0.290785 0.290785

0.49161 0.491772 0.866687 0.532859 0.540645 0.540645 0.540645 0.491566 0.49161 0.491772 0.540645 0.532859 0.634943 0.491566 0.485918 0.491772 0.486383 0.486378 0.531202 0.478009 0.486378 0.621998 0.483776 0.793898 0.482351 0.719768 0.482351 0.459983 0.45999 0.449766 0.491566 0.485918 0.49161 0.459978 0.45999 0.449766 0.459978 0.459983 0.449766 0.761661 0.476457 0.478009 0.486383 0.718288 0.476457 0.719768 0.793898 0.570171 0.558082 0.570172 0.558082 0.585809 0.585796 0.459978 0.459983 0.45999 0.508112 0.53628

24

0.21492 0.215082 0.4965 0.200043 0.207828 0.200002 0.200002 0.2 0.200044 0.200206 0.214006 0.20622 0.332107 0.218479 0.21283 0.218685 0.200007 0.200002 0.200001 0.200002 0.208371 0.353749 0.215527 0.51282 0.201273 0.443012 0.205595 0.210276 0.210284 0.200059 0.205649 0.2 0.205693 0.221089 0.221102 0.210877 0.217742 0.217747 0.20753 0.496303 0.211098 0.207523 0.215897 0.441831 0.2 0.368377 0.442507 0.270897 0.258808 0.212112 0.200022 0.200074 0.200061 0.200001 0.200007 0.200014 0.217326 0.245495

31 31 32 32 33 33 34 34 35 35 36 37 38 39 40 41 41 42

27 29 33 42 21 23 31 42 25 28 38 35 40 37 41 31 33 39

0.308096 0.308096 0.3335 0.3335 0.446322 0.446322 0.380986 0.380986 0.370171 0.370171 0.321161 0.379027 0.413861 0.386384 0.416125 0.408193 0.408193 0.277435

0.508112 0.585809 0.608211 0.583725 0.718288 0.761661 0.608195 0.583725 0.570172 0.570171 0.521736 0.579248 0.613861 0.586388 0.616131 0.608195 0.608211 0.477435

0.200015 0.277712 0.274711 0.250225 0.271965 0.315339 0.227209 0.202739 0.200001 0.2 0.200575 0.200221 0.2 0.200005 0.200006 0.200002 0.200018 0.2

The convergence characteristics of MWCA and WCA algorithms are shown in Fig. 10. From this figure, it can be observed that the MWCA algorithm gives better convergence compared with WCA algorithm. The optimal solution with MWCA is 13.308 s, while the solution obtained with WCA, BBO, BH, PSO, DE, EFO, MEFO, CSA, GA, FFA, and BSA are 18 s, 16.58 s, 35.44 s, 41.46 s, 17.2 s, 17.9 s, 13.953 s, 19.552 s, 26.07 s, 22.71 s, and 16.293 s, respectively. The MWCA reaches to the minimum objective function (13.308 s) after computation time about 390.3s and 2853 iterations while the WCA reaches to the minimum objective function (18 s) after computation time about 495.8 s and 2975 iterations.

25

MWCA

WCA

65

Objective Function (s)

55

45

35

25

15

1 89 177 265 353 441 529 617 705 793 881 969 1057 1145 1233 1321 1409 1497 1585 1673 1761 1849 1937 2025 2113 2201 2289 2377 2465 2553 2641 2729 2817 2905 2993

5

Iterations

Fig. 10. Convergence characteristics of MWCA and WCA (15-bus system)

The statistical evaluation of the results obtained by different optimization techniques is presented in Table 9. This table gives the best, the worst, and the mean values of the objective function with its standard deviation obtained by MWCA, EFO, MEFO, BH, BBO, GA, GANLP, FFA, and HS. From this table, it can be observed that the worst value obtained by the proposed algorithm (13.618 s) of the objective function are close to the best value (13.308 s), which indicate the robustness of the MWCA. The standard deviation for the MWCA is lower than EFO, MEFO, BH, BBO, GA, and GA-NLP which indicates the high robustness of MWCA compared with these algorithms. The objective function for 30 individual runs of the proposed algorithm are calculated and graphically presented in Fig. 11. This figure proves the robustness the proposed algorithm for different runs.

26

Table 9 Statistical analysis of 15-bus system Parameters

MWCA

EFO

MEFO

BH

BBO

GA

GA-NLP

FFA

HS

Mean

13.546

20.475

16.573

38.41

17.984

28.69

20.129

22.829

19.62

Standard Deviation Worst Best Number of Runs Violation

0.069

0.880

1.576

1.310

0.765

1.888

0.3853

0.1045

0.0103

13.618 13.308 30

21.691 17.906 30

20.203 13.953 30

40.56 35.44 30

19.453 16.58 30

32.715 26.073 50

20.984 19.584 50

22.991 22.717 50

19.69 19.62 50

0

0

0

0

0

0

0

0

0

Objective Function (s)

19 17 15 13 11 9 7 5 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Run Number

Fig. 11.The objective function obtained by MWCA during 30 different runs (15-bus system)

4.4. Case 4: IEEE 30-bus test system The last test system considered in this section is the IEEE 30-bus system. The single line diagram of this system is shown in Fig. 12. This system consists of 38 relays, 62 of primary and backup relay pairs, and 76 optimization variables. The initial ranges for

and

are 0.1 and 1.1, respectively. The PSmin and PSmax limits are 1.5 and 6, respectively, and the CT ratio for each relay is 1000:5. The CTI is set to 0.3 s. More details of this system such as; fault currents and primary and the backup relationship of relay pairs can be found in [36].

27

7 R26

R27

M

M

R8

L8

33kV

R7 L7

R25 6 L6

5

16

R6 R39

R24

L5

DG

15

R5

4

R23

R18

L19 L18

R19

14 R36

R34

R35 11 R15 M

R32

L15

M

R4

L4

L17

DG

L13

R22

L3 10

R13

R21

R30 R3

L16 2

R20

L11 12

R14

L14

R16

R31

9

L10 L12

R33

R17

L2

L1 R29

R12

13

R28

L9

R10

R9

R1 R2

8

1

33kV

33kV

Fig. 12. Single line diagram of IEEE 30-bus test system.

Table 10 Optimal relay settings of IEEE 30-bus system Relay No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

PS 4.367038 3.570571 4.121582 4.784506 3.272633 3.26221 2.73716 2.30285 4.804753 4.155365 3.74141 4.254808 3.790042 3.878774 2.737265 3.665026 2.955374 3.875187 4.36711

TDS 0.197309 0.130813 0.155554 0.128203 0.127392 0.100053 0.1 0.100001 0.190083 0.183643 0.157674 0.131211 0.136254 0.117261 0.120383 0.2045 0.100004 0.121026 0.137226

28

3

2.77291 2.571723 4.15129 3.5206 3.277607 2.805266 1.5 1.500263 3.350611 3.542625 3.306794 3.858165 3.664886 3.471069 2.844028 3.464648 1.854361 3.256917 3.828449 18.69

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 𝐢 𝟏

𝐢

(s)

0.1 0.1 0.139932 0.135727 0.112622 0.164138 0.100095 0.100027 0.125475 0.1 0.130416 0.107665 0.122285 0.157693 0.180215 0.133096 0.1 0.128931 0.126545

Table 11 Primary and backup operating time of relays and CTI of IEEE 30-bus system Relay pairs 1 1 1 2 2 2 3 4 4 5 5 6 7 8 9 9 9 10 10 10 11 12 13 14 15 16 16 17 17 18 18 19

21 28 29 20 28 29 1 2 3 4 37 5 6 6 20 21 29 20 21 28 10 9 11 12 13 14 36 14 35 4 24 15

𝐫𝐢 𝐚𝐫 (s) 0.737062 0.737062 0.737062 0.488662 0.488662 0.488662 0.581081 0.478911 0.478911 0.47588 0.47588 0.373753 0.373557 0.373559 0.710068 0.710068 0.710068 0.686009 0.686009 0.686009 0.589003 0.490147 0.508985 0.438035 0.449697 0.763922 0.763922 0.373573 0.373573 0.452102 0.452102 0.512618

(s) 𝐚 2.277072 1.037067 1.042352 1.083293 1.042075 1.048553 0.881323 0.825634 0.778914 0.776137 0.809906 0.673948 0.686625 0.692884 1.010418 2.063872 1.044179 1.020878 2.108282 1.048474 0.889014 0.79015 0.808996 0.738591 0.750135 1.063939 2.48959 1.087288 0.921487 0.775954 0.810518 0.812942

29

𝐂 1.54001 0.300005 0.305291 0.594631 0.553413 0.559891 0.300242 0.346723 0.300003 0.300257 0.334026 0.300194 0.313068 0.319325 0.300349 1.353804 0.334111 0.334869 1.422273 0.362465 0.300011 0.300003 0.300011 0.300556 0.300438 0.300018 1.725669 0.713715 0.547914 0.323851 0.358416 0.300324

19 19 20 21 21 22 22 23 23 24 26 27 28 29 30 31 32 33 33 34 34 34 35 35 35 36 36 36 37 38

16 17 22 3 23 2 23 24 37 25 8 7 31 30 32 33 34 35 36 16 17 38 15 17 38 15 16 38 19 18

0.512618 0.512618 0.373557 0.373557 0.373557 0.522725 0.522725 0.507015 0.507015 0.420705 0.37391 0.373657 0.468721 0.373557 0.487178 0.402189 0.456803 0.589072 0.589072 0.673205 0.673205 0.673205 0.497189 0.497189 0.497189 0.373557 0.373557 0.373557 0.48163 0.472715

0.97225 2.293523 0.673569 0.784028 0.826654 0.822732 0.822956 0.807322 0.80708 0.720705 0.866127 0.700564 0.768949 0.673575 0.787268 0.702189 0.756967 0.88918 2.326729 0.973208 2.30491 0.973373 0.809867 2.364859 0.967707 0.822326 0.989234 0.984581 0.781655 0.772839

0.459632 1.780905 0.300012 0.410471 0.453097 0.300008 0.300231 0.300307 0.300064 0.3 0.492217 0.326906 0.300228 0.300018 0.30009 0.3 0.300163 0.300107 1.737656 0.300003 1.631705 0.300168 0.312678 1.86767 0.470518 0.448769 0.615678 0.611024 0.300025 0.300123

The convergence characteristics of MWCA and WCA algorithms are shown in Fig. 13. From this figure, it can be observed that the MWCA algorithm gives better convergence compared to WCA. The optimal solution obtained by MWCA is 18.69 s, while the solution obtained with WCA, GA, PSO, HS, SOA, GSA, and GSA-SQP are 31.415 s, 28.019 s, 19.213 s, 33.773 s, 51.774 s, and 26.825 s, respectively. The MWCA reaches to the minimum objective function (18.69 s) after computation time about 316.7 s and 2890 iterations while the WCA reaches to the minimum objective function (31.415 s) after computation time about 457.8 s and 2860 iterations.

30

MWCA

WCA

Objective Function (s)

210

160

110

60

1 89 177 265 353 441 529 617 705 793 881 969 1057 1145 1233 1321 1409 1497 1585 1673 1761 1849 1937 2025 2113 2201 2289 2377 2465 2553 2641 2729 2817 2905 2993

10

Iteration

Fig. 13. Convergence characteristics of the MWCA and WCA (IEEE 30-bus system)

The statistical evaluation of the results obtained by different optimization techniques is presented in Table 12. This table gives the best, the worst, and the mean values of the objective function along with its standard deviation obtained by MWCA, GA, PSO, HS, SOA, GSA, and GSA-SQP. Among all these techniques, it is observed that the MWCA gives the least standard deviation (0.337). The objective function for 100 individual runs of the proposed algorithm are calculated and graphically presented in Fig. 14. This figure proves the robustness the proposed algorithm for different runs. Table 12 Statistical analysis of IEEE 30-bus system Parameters Mean Standard Deviation Worst Best Number of Runs Violation

MWCA 19.753 0.337 20.173 18.69 100 0

GA 29.223 0.671 30.37 28.019 100 0

PSO 46.085 6.168 58.569 39.183 100 0

31

HS 19.711 0.362 20.2305 19.213 100 0

SOA 35.8641 2.077 40.781 33.773 100 0

GSA 4.921 66.956 51.774 10 0

GSA-SQP 0.98 29.689 26.825 10 0

40

Objective Function (s)

35 30 25 20 15 10 5

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

0

Run Number

Fig. 14. The objective function obtained by MWCA for 100 different runs (IEEE 30-bus system)

4.5. Verification of MWCA using DIgSILENT PowerFactory Three phase faults at both ends of transmission line 2 in 15-bus test system are applied and implemented DIgSILENT PowerFactory 14 [37], to verify the results obtained by the proposed MWCA. Three phase fault currents are applied near relay 9 (see Fig. 9). The operating time for primary and backup relays using DIgSILENT PowerFactory is shown in Fig. 15. From this figure, it can be observed that primary relay (relay 9) operates at 0.33 s and backup relays (relay 5 and relay 8) operate at 0.54 s and 0.53 s, respectively. Also, it can be observed that there is sufficient time margin for backup relays to operate more than 0.2 s. Three phase fault currents are also applied near relay 10 (see Fig. 9). The operating time for primary and backup relays using DIgSILENT PowerFactory is shown in Fig. 16. From this figure, it can be observed that primary relay (relay 10) operates at 0.31 s and backup relay (relay 14) operates at 0.65 s. Also, it can be observed that there is sufficient time margin for backup relay to operate more than 0.2 s as show in Fig. 16. The operating times obtained using DIgSILENT PowerFactory are similar with those obtained by the proposed MWCA.

32

for relays 5, 8, and 9 (15-bus system)

Operating Time (s)

Fig. 15. Operating time

Fault Current (A)

Fig. 16. Operating time for relays 10 and 14 (15-bus system).

5. Conclusion In this paper, a modified version of the Water Cycle Algorithm, called MWCA has been proposed to solve the coordination problem of DOCRs. The proposed technique based on

33

updating the C-value according to iteration number instead of constant value. The performance of the proposed algorithm has been validated using four test systems. The results obtained by the proposed algorithm has been validated using benchmark DIgSILENT PowerFactory. Based on the results obtained by MWCA, WCA and other well-known optimization techniques (EFO, MEFO, GA, BBO FFA, BH, GA-NLP, HS, SOA, GSA, and GSA-SQP), the proposed MWCA is able to find the best relay setting, satisfy coordination margin, and minimize the total operating time of all primary relays. In addition, the proposed algorithm converges to the global minimum faster than the traditional WCA. The proposed optimization technique can be extended to other applications including optimal power flow and optimal allocation of compensation devices to achieve multi-objective functions. References [1] A. Tjahjono, D. O. Anggriawan, A. K. Faizin, A. Priyadi, M. Pujiantara, T. Taufik, et al., ‘Adaptive modified firefly algorithm for optimal coordination of overcurrent relays’, IET Generation, Transmission & Distribution, 2017, 11, pp. 2575-2585. [2] M. Hussain, S. Rahim, and I. Musirin, ‘Optimal overcurrent relay coordination: a review’, Procedia Engineering, 2013, 53, pp. 332-336. [3] A. G. Phadke and J. S. Thorp, ‘Computer relaying for power systems’, John Wiley & Sons, 2009. [4] A. R. Al-Roomi and M. E. El-Hawary, ‘Optimal coordination of directional overcurrent relays using hybrid BBO-LP algorithm with the best extracted time-current characteristic curve’, Electrical and Computer Engineering, IEEE 30th Canadian Conference on, 2017, pp.1-6. [5] H. Bouchekara, M. Zellagui, and M. A. Abido, ‘Optimal coordination of directional overcurrent relays using a modified electromagnetic field optimization algorithm’, Applied Soft Computing, 2017, 54, pp. 267-283, [6] T. Amraee, ‘Coordination of directional overcurrent relays using seeker algorithm’, IEEE Transactions on Power Delivery, 2012, 27, pp. 1415-1422.

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[17] A. E. L. Rivas and L. A. G. Pareja, ‘Coordination of directional overcurrent relays that uses an ant colony optimization algorithm for mixed-variable optimization problems’, Environment and Electrical Engineering Industrial and Commercial Power Systems Europe (EEEIC/I&CPS Europe), IEEE International Conference, 2017, pp. 1-6. [18] A. Hatamlou, "Black hole: A new heuristic optimization approach for data clustering," Information sciences, vol. 222, pp. 175-184, 2013. [19] H. Abedinpourshotorban, S. M. Shamsuddin, Z. Beheshti, and D. N. Jawawi, "Electromagnetic field optimization: A physics-inspired metaheuristic optimization algorithm," Swarm and Evolutionary Computation, vol. 26, pp. 8-22, 2016. [20] M. Zellagui and A. Y. Abdelaziz, ‘Optimal Coordination of Directional Overcurrent Relays using Hybrid PSO-DE Algorithm’, International Electrical Engineering Journal (IEEJ), 2015, 6, pp. 1841-1849. [21] E. Rashedi, H. Nezamabadi-Pour, and S. Saryazdi, "GSA: a gravitational search algorithm," Information sciences, vol. 179, pp. 2232-2248, 2009. [22] V. Rajput, K. Pandya, and K. Joshi, ‘Optimal coordination of Directional Overcurrent Relays using

hybrid

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method’,

Electrical

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