# Nature-Inspired Whale Optimization Algorithm for Optimal Coordination of Directional Overcurrent Relays in Power Systems

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation and Incitement

#### 1.2. Literature Review

#### 1.3. Contribution and Paper Organization

## 2. DOCR Problem Formulation

#### 2.1. Coordination Criteria

- T
_{b}: the backup relay operating time; and - T
_{p}: the primary (or main) relay operating time.

#### 2.2. Relay Setting Bounds

## 3. Whale Optimization Algorithm

#### 3.1. Encircling Prey

#### 3.2. Bubble-Net Attacking Method

#### 3.2.1. Shrinking Encircling Mechanism

#### 3.2.2. Spiral Updating of Position

#### 3.3. Search for Prey

#### 3.4. The Steps of WOA

Algorithm 1. The pseudocode of WOA. |

Initialize population size (NP), number of design variables and meeting criteria, number of fitness function evaluations Analyze the fitness function value for each search agent ${\mathrm{X}}^{*}$ = The best search agent while (t < maximum number of iteration)for each search agentUpdate a, $\overrightarrow{A}$, C, l and p if (p < 0.5)if (|$\overrightarrow{A}$| < 1)Update the position of the current search agent by the Equation (6) else if (|$\overrightarrow{A}$| $\ge $1Select the random search agent ${\mathrm{X}}_{\mathrm{rand}}$ Update the position of the current search agent by the Equation (13) end ifelse if (p $\ge 0.5$)Update the position of the current search agent by the Equation (10) end ifend forAlleviate any search agent that goes outside the search space fitness function evaluations of each search agent Update ${\mathrm{X}}^{*}$ if there is a better solution t = t + 1 end whileReturn ${\mathrm{X}}^{*}$ |

## 4. Results and Discussion

#### 4.1. Case I: IEEE Three-Bus System

#### 4.2. Case II: IEEE Eight-Bus System

#### 4.3. Case III: IEEE Nine-Bus System

#### 4.4. Case IV: IEEE 15-Bus System

#### 4.5. Case V: IEEE 30-Bus System

#### 4.6. Case VI: Coordination Scheme Using Numerical Directional Relays

#### Application of WOA

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

OCR | Overcurrent relay |

DOCR | Directional overcurrent relay |

TDS | Time dial setting |

T_{op} | Total operating time |

PSM | Plug setting multiplier |

I_{f} | Fault current |

I_{p} | Pickup current |

CTR | Current transformer ratio |

CTI | Coordination time interval |

DG | Distributed generation |

IDMT | Inverse definite minimum time |

IEC | International electro-technical commission |

IEEE | Institute of electrical and electronics engineers |

NERC | Federal energy regulatory commission |

PR | Primary relay |

BR | Backup relay |

T_{b} | Backup relay operating time |

T_{p} | Primary relay operating time |

LP | Linear programming |

NLP | Non-linear programming |

MILP | Mixed integer linear programming |

MINLP | Mixed integer non-linear programming |

MECPSO | Multiple embedded crossover PSO |

FA | Firefly algorithm |

GA | Genetic algorithm |

HGA | Hybrid genetic algorithm |

DE | Differential evaluation |

MEFO | Modified electromagnetic field optimization |

PSO | Particle swarm optimization |

BBO | Biogeography based optimization |

GWO | Grey wolf optimization |

TLBO | Teaching learning based optimization |

SA | Seeker algorithm |

GSO | Group search optimization |

AP | Analytic approach |

BSA | Back tracking search algorithm |

WOA | Whale optimization algorithm |

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Relay No. | CTR | Pickup Tap |
---|---|---|

1 | 300/5 | 5 |

2 | 200/5 | 1.5 |

3 | 200/5 | 5 |

4 | 300/5 | 4 |

5 | 200/5 | 2 |

6 | 400/5 | 2.5 |

Relay No. | TDS | PS |
---|---|---|

1 | 0.0500 | 1.2500 |

2 | 0.0500 | 1.2500 |

3 | 0.05553 | 1.3837 |

4 | 0.0500 | 1.2500 |

5 | 0.0710 | 2.4746 |

6 | 0.1587 | 2.2163 |

Total Operating Time (s) | 1.5262 |

Method | Objective Function |
---|---|

TLBO (MOF) [39] | 6.972 |

TLBO [39] | 5.3349 |

MDE [37] | 4.7806 |

Simplex method [29] | 1.9258 |

MINLP [28] | 1.727 |

Seeker algorithm [28] | 1.599 |

PSO method [34] | 1.9258 |

BB0-LP [40] | 1.59871 |

GSO [47] | 1.4807 |

Proposed algorithm | 1.5262 |

**Table 4.**Comparison of total net gain in time achieved by WOA with the methods used in the literature for IEEE three-bus system.

Net Gain | ∑ ∆(t) (s) |
---|---|

WOA/TLBO (MOF) | 5.4458 |

WOA/TLBO | 3.8087 |

WOA/MDE | 3.2544 |

FWOA/SM | 0.3996 |

WOA/MINLP | 0.2008 |

WOA/SA | 0.0728 |

WOA/PSO | 0.3996 |

WOA/BBO-LP | 0.07251 |

Relay No. | CTR |
---|---|

1 | 1200/5 |

2 | 1200/5 |

3 | 800/5 |

4 | 1200/5 |

5 | 1200/5 |

6 | 1200/5 |

7 | 800/5 |

8 | 1200/5 |

9 | 800/5 |

10 | 1200/5 |

11 | 1200/5 |

12 | 1200/5 |

13 | 1200/5 |

14 | 800/5 |

Relay No. | TDS | PS |
---|---|---|

1 | 0.1000 | 1.25 |

2 | 0.5929 | 1.3746 |

3 | 0.1007 | 1.2586 |

4 | 0.1000 | 1.25 |

5 | 0.3581 | 2.0638 |

6 | 0.2490 | 1.5745 |

7 | 0.1018 | 1.2726 |

8 | 0.3430 | 1.8559 |

9 | 0.1000 | 1.25 |

10 | 0.1000 | 1.25 |

11 | 0.1004 | 1.2548 |

12 | 0.1521 | 1.901 |

13 | 0.1000 | 1.25 |

14 | 0.1000 | 1.25 |

Total operating time (s) | 5.9535 |

**Table 7.**Comparison of the WOA result with the methods used in the literature for the IEEE eight-bus system.

Method | Objective Function |
---|---|

SA [28] | 8.4270 |

GA [14] | 11.001 |

HGA-LP [14] | 10.9499 |

NLP [2] | 6.4169 |

LM [2] | 11.0645 |

BBO-LP [40] | 8.75559 |

MILP [42] | 8.0061 |

FA [43] | 6.6463 |

MEFO [44] | 6.349 |

BSA [41] | 6.363 |

Proposed algorithm | 5.9535 |

**Table 8.**Comparison of total net gain in time achieved by WOA with the methods used in the literature for the IEEE eight-bus system.

Net Gain | ∑ ∆(t) (s) |
---|---|

WOA/SA | 2.4735 |

WOA/GA | 5.0475 |

WOA/HGA-LP | 4.9964 |

WOA/NLP | 0.45819 |

WOA/LP | 5.111 |

WOA/BBO-LP | 2.8020 |

WOA/FA | 0.6929 |

WOA/MEFO | 0.3955 |

WOA/BSA | 0.4095 |

Relay No. | TDS | PS |
---|---|---|

1 | 0.2316 | 2.4466 |

2 | 0.1001 | 1.5014 |

3 | 0.2377 | 2.4650 |

4 | 1.200 | 2.5000 |

5 | 0.1469 | 2.2553 |

6 | 0.7059 | 2.5000 |

7 | 0.1761 | 2.4542 |

8 | 0.5674 | 2.4224 |

9 | 1.2000 | 2.5000 |

10 | 0.2193 | 2.3922 |

11 | 0.6990 | 1.8076 |

12 | 0.1368 | 1.8399 |

13 | 0.1454 | 2.1276 |

14 | 0.1497 | 2.5000 |

15 | 0.1632 | 2.0901 |

16 | 1.1431 | 2.3815 |

17 | 0.2636 | 1.6991 |

18 | 0.14875 | 2.2135 |

19 | 0.12251 | 1.8376 |

20 | 0.18656 | 2.4963 |

21 | 0.51479 | 1.5402 |

22 | 0.17653 | 2.5000 |

23 | 1.2000 | 2.5000 |

24 | 0.1303 | 1.9311 |

Total operating time (s) | 8.3849 |

**Table 10.**Comparison of the WOA result with the methods used in the literature for the IEEE-9 bus system.

Method | Objective Function |
---|---|

TLBO [45] | 82.9012 |

IDE [45] | 59.6471 |

MTALBO [45] | 41.9041 |

GA [13] | 32.6058 |

BBO [40] | 28.8348 |

BH [44] | 25.884 |

NPL [13] | 19.4041 |

PSO [48] | 13.9742 |

HS [44] | 9.838 |

DE [48] | 8.6822 |

Proposed algorithm | 8.3849 |

**Table 11.**Comparison of total net gain in time achieved by the WOA with the methods used in the literature for the IEEE nine-bus system.

Net Gain | ∑ ∆(t) (s) |
---|---|

WOA/TLBO | 74.5163 |

WOA/IDE | 51.2622 |

WOA/MTALBO | 33.5192 |

WOA/GA | 24.2209 |

WOA/BBO | 20.4499 |

WOA/BH | 17.4991 |

WOA/NPL | 11.0192 |

WOA/PSO | 5.5893 |

WOA/HS | 1.4531 |

WOA/DE | 0.2973 |

Relay No. | CT Ratio |
---|---|

18-20-21-29 | 1600/5 |

2-4-8-11-12-14-15-23 | 1200/5 |

1-3-5-10-13-19-36-37-40-42 | 800/5 |

6-7-9-16-24-25-26-27-28-31-32-33-35 | 600/5 |

17-22-30-34-38-39-41 | 400/5 |

Relay No. | WOA | Relay No. | WOA | ||
---|---|---|---|---|---|

TDS | PS | TDS | PS | ||

1 | 0.1000 | 0.5000 | 22 | 0.1039 | 0.5195 |

2 | 0.1030 | 0.5150 | 23 | 0.1010 | 0.5049 |

3 | 0.1078 | 0.5393 | 24 | 0.1000 | 0.5000 |

4 | 0.1000 | 0.5000 | 25 | 0.1139 | 0.5695 |

5 | 0.1041 | 0.5206 | 26 | 0.1101 | 0.5504 |

6 | 0.1240 | 0.6201 | 27 | 1.0414 | 2.3668 |

7 | 0.1000 | 0.5003 | 28 | 0.3260 | 1.1297 |

8 | 0.1000 | 0.5000 | 29 | 0.2249 | 0.7461 |

9 | 0.1455 | 0.7275 | 30 | 0.1000 | 0.5000 |

10 | 0.1078 | 0.5392 | 31 | 0.1483 | 0.5000 |

11 | 0.1020 | 0.5103 | 32 | 0.1056 | 0.5280 |

12 | 0.1000 | 0.5000 | 33 | 0.1487 | 0.7438 |

13 | 0.1070 | 0.5350 | 34 | 0.2123 | 0.5689 |

14 | 1.1000 | 2.5000 | 35 | 0.1152 | 0.5759 |

15 | 0.1000 | 0.5000 | 36 | 0.7140 | 1.6790 |

16 | 0.1148 | 0.5742 | 37 | 0.1245 | 0.6229 |

17 | 0.1015 | 0.5077 | 38 | 0.1066 | 1.1121 |

18 | 0.4930 | 1.4766 | 39 | 0.4113 | 0.9377 |

19 | 0.1539 | 0.7699 | 40 | 0.1515 | 0.7576 |

20 | 0.2644 | 0.9671 | 41 | 0.4033 | 0.9166 |

21 | 0.1557 | 0.7785 | 42 | 0.1105 | 0.5195 |

${T}_{op}$ (s) | 11.2670 |

**Table 14.**Comparison of the WOA result with the methods used in the literature for the IEEE 15-bus system.

Method | Objective Function |
---|---|

MTLBO [45] | 52.5039 |

SA [28] | 12.227 |

MINLP [28] | 15.335 |

AP [46] | 11.6542 |

GSO [47] | 13.6542 |

IGSO [47] | 12.135 |

DE [48] | 11.7591 |

HS [48] | 12.6225 |

MEFO [44] | 13.953 |

BSA [41] | 16.293 |

Proposed algorithm | 11.2670 |

**Table 15.**Comparison of total net gain in time achieved by the WOA with the methods used in the literature for the IEEE 15-bus system.

Net Gain | ∑ ∆(t) (s) |
---|---|

WOA/TLBO | 41.2369 |

WOA/SA | 0.96 |

WOA/MINPL | 4.068 |

WOA/AP | 0.3872 |

WOA/GSO | 2.3872 |

WOA/IGSO | 0.868 |

WOA/DE | 0.4921 |

WOA/HS | 1.3555 |

WOA/MEFO | 2.686 |

WOA/BSA | 5.026 |

Fault Zone | Primary Relay | Primary Relay |
---|---|---|

L 1 | 1 | 4, 18, 20 |

2 | 6 | |

L2 | 3 | 2, 18, 20 |

4 | 5, 8 | |

L 3 | 5 | 1 |

6 | 3, 8 | |

L 4 | 7 | 3, 5 |

8 | 10, 36 | |

L 5 | 9 | 7, 36 |

10 | 12 | |

L 6 | 11 | 9 |

12 | - | |

L 7 | 13 | 11 |

14 | 15 | |

L 8 | 15 | 11 |

16 | 13 | |

L 9 | 17 | 2, 4, 20 |

18 | 24 | |

L 10 | 19 | 2, 4, 18 |

20 | 22 | |

L 11 | 21 | 19 |

22 | 26 | |

L 12 | 23 | 17 |

24 | 28 | |

L 13 | 25 | 21 |

26 | 30 | |

L 14 | 27 | 23 |

28 | 32, 34 | |

L 15 | 29 | 25 |

30 | 31, 33, 38 | |

L 16 | 31 | 27, 34 |

32 | 29, 33, 38 | |

L 17 | 33 | 27, 32 |

34 | 37 | |

L 18 | 35 | 29, 31, 38 |

36 | 7, 10 | |

L 19 | 37 | 37 |

38 | 29, 31, 33 | |

L 20 | 39 | 35 |

- | - |

Relay No. | TDS | PS |
---|---|---|

1 | 0.1131 | 1.6958 |

2 | 0.1000 | 1.5000 |

3 | 0.1007 | 1.5109 |

4 | 0.1007 | 1.5111 |

5 | 0.1000 | 1.5000 |

6 | 0.9236 | 2.4761 |

7 | 0.1000 | 1.5005 |

8 | 0.1000 | 1.5000 |

9 | 0.1001 | 1.5029 |

10 | 0.1002 | 1.5042 |

11 | 0.1076 | 1.6149 |

12 | 0.1000 | 1.5000 |

13 | 0.1074 | 1.6118 |

14 | 1.0933 | 2.4849 |

15 | 0.6461 | 2.3447 |

16 | 0.8541 | 1.9412 |

17 | 0.2737 | 1.7453 |

18 | 0.6984 | 2.1623 |

19 | 0.1046 | 1.5824 |

20 | 0.2328 | 2.4762 |

21 | 0.1672 | 2.3334 |

22 | 0.1118 | 1.6782 |

23 | 0.1003 | 1.5000 |

24 | 0.1000 | 1.5000 |

25 | 0.1013 | 1.5205 |

26 | 0.1757 | 2.3145 |

27 | 0.1037 | 1.5555 |

28 | 0.2170 | 2.3228 |

29 | 0.1990 | 2.1887 |

30 | 0.2856 | 2.5000 |

31 | 0.3598 | 2.0241 |

32 | 0.1049 | 1.5747 |

33 | 0.1522 | 2.1039 |

34 | 0.1000 | 1.5006 |

35 | 0.2242 | 2.4661 |

36 | 0.1271 | 1.9075 |

37 | 0.1727 | 2.4772 |

38 | 0.2007 | 1.7111 |

39 | 0.1002 | 1.5035 |

Total operating time (s) | 15.7139 |

**Table 18.**Comparison of the proposed WOA with the methods used in the literature for the IEEE 30-bus system.

Method | Objective Function |
---|---|

GA [48] | 28.0195 |

PSO [48] | 39.1836 |

DE [48] | 17.8122 |

HS [48] | 19.2133 |

SOA [48] | 33.7734 |

Proposed Algorithm | 15.7139 |

**Table 19.**Comparison of total net gain in time achieved by the WOA with the methods used in the literature for the IEEE 30-bus system.

Net Gain | ∑ ∆(t) (s) |
---|---|

WOA/GA | 12.3056 |

WOA/PSO | 23.4697 |

WOA/DE | 2.0983 |

WOA/HS | 3.4994 |

WOA/SOA | 18.0595 |

CT Ratio | Relay No. | CT Ratio | Relay No. |
---|---|---|---|

8000/5 | 1 | 1000/5 | 20, 35, 38 |

5000/5 | 29 | 800/5 | 16,18 |

4000/5 | 5, 25 | 600/5 | 22, 32, 37, 40 |

3500/5 | 3, 14 | 500/5 | 17, 26, 34 |

3000/5 | 21 | 400/5 | 2, 4, 8, 10, 13, 24 |

2500/5 | 7 | 250/5 | 11 |

2000/5 | 12,36,39 | 200/5 | 6 |

1600/5 | 9, 19, 23, 27, 31 | 50/5 | 28 |

1200/5 | 15, 30, 33 | - | - |

Relay No. | TDS | PS |
---|---|---|

1 | 0.1000 | 0.5000 |

2 | 0.1000 | 0.5000 |

3 | 1.0227 | 1.9967 |

4 | 0.1000 | 0.5000 |

5 | 1.1000 | 2.0000 |

6 | 1.0703 | 1.9461 |

7 | 0.1000 | 0.5000 |

8 | 0.1010 | 0.5048 |

9 | 0.1316 | 0.6582 |

10 | 0.2419 | 1.1192 |

11 | 0.1097 | 0.5486 |

12 | 0.1154 | 0.5773 |

13 | 0.1000 | 0.5000 |

14 | 1.0968 | 1.9941 |

15 | 0.1146 | 0.5731 |

16 | 0.1107 | 0.5539 |

17 | 0.1000 | 0.5001 |

18 | 0.5058 | 1.9887 |

19 | 1.0551 | 1.9185 |

20 | 0.1145 | 0.5727 |

21 | 0.2439 | 1.2169 |

22 | 0.1379 | 0.6897 |

23 | 0.2896 | 0.5218 |

24 | 0.2923 | 1.4617 |

25 | 0.3049 | 1.7079 |

26 | 1.1000 | 2.0000 |

27 | 0.1014 | 0.5071 |

28 | 0.1021 | 0.5108 |

29 | 0.1000 | 0.5000 |

30 | 0.8158 | 1.9280 |

31 | 1.0175 | 1.9850 |

32 | 1.0721 | 1.9508 |

33 | 0.1278 | 0.6390 |

34 | 0.1264 | 0.6324 |

35 | 0.1620 | 0.8101 |

36 | 1.0557 | 1.9810 |

37 | 0.1710 | 0.8283 |

38 | 0.2721 | 0.5000 |

39 | 0.9686 | 1.7611 |

40 | 0.13037 | 0.6518 |

Total operating time (s) | 9.9105 |

**Table 22.**Comparison of the proposed WOA with the methods used in the literature for the IEEE 14-bus system.

Method | Objective Function |
---|---|

HGA-LP [42] | 13.4914 |

MILP [42] | 13.1411 |

MECPSO [49] | 12.919 |

MAPSO [49] | 14.126 |

Proposed Algorithm | 9.9105 |

**Table 23.**Comparison of total net gain in time achieved by the WOA with the methods used in the literature for the IEEE 14-bus system.

Net Gain | ∑ ∆(t) (s) |
---|---|

WOA/HGA-LP | 3.5812 |

WOA/MILP | 3.2306 |

WOA/MECPSO | 3.0085 |

WOA/MAPSO | 4.2155 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wadood, A.; Khurshaid, T.; Farkoush, S.G.; Yu, J.; Kim, C.-H.; Rhee, S.-B. Nature-Inspired Whale Optimization Algorithm for Optimal Coordination of Directional Overcurrent Relays in Power Systems. *Energies* **2019**, *12*, 2297.
https://doi.org/10.3390/en12122297

**AMA Style**

Wadood A, Khurshaid T, Farkoush SG, Yu J, Kim C-H, Rhee S-B. Nature-Inspired Whale Optimization Algorithm for Optimal Coordination of Directional Overcurrent Relays in Power Systems. *Energies*. 2019; 12(12):2297.
https://doi.org/10.3390/en12122297

**Chicago/Turabian Style**

Wadood, Abdul, Tahir Khurshaid, Saeid Gholami Farkoush, Jiangtao Yu, Chang-Hwan Kim, and Sang-Bong Rhee. 2019. "Nature-Inspired Whale Optimization Algorithm for Optimal Coordination of Directional Overcurrent Relays in Power Systems" *Energies* 12, no. 12: 2297.
https://doi.org/10.3390/en12122297