3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 34 Vol. 9 N.º 2 Junio - Septiembre

NUMERICAL DATA FOR WIND TURBINE MICROSITING

INSPIRED BY HUMAN DYNASTIES BY USE OF THE

DYNASTIC OPTIMIZATION ALGORITHM (DOA)

Shaq-ur-Rehman Massan

QEC and Coordination

Mohammad Ali Jinnah University, Karachi and

Shaheed Zulkar Ali Bhutto Institute of Science and Technology, Karachi, (Pakistan).

E-mail: srmassan@hotmail.com ORCID: https://orcid.org/0000-0001-6548-6513

Asim Imdad Wagan

Department of Engineering

Mohammad Ali Jinnah University, Karachi, (Pakistan).

E-mail: aiwagan@gmail.com ORCID: https://orcid.org/0000-0001-9765-5385

Muhammad Mujtaba Shaikh

Department of Basic Sciences and Related Studies

Mehran University of Engineering and Technology, Jamshoro, (Pakistan).

E-mail: mujtaba.shaikh@faculty.muet.edu.pk ORCID: https://orcid.org/0000-0002-1471-822X

Recepción:

13/02/2020

Aceptación:

08/04/2020

Publicación:

15/06/2020

Citación sugerida:

Massan, S.-U.-R., Wagan, A. I., y Shaikh, M. M. (2020). Numerical data for wind turbine micrositing inspired by

human dynasties by use of the Dynastic Optimization Algorithm (DOA). 3C Tecnología. Glosas de innovación aplicadas a la

pyme, 9(2), 71-85. http://doi.org/10.17993/3ctecno/2020.v9n2e34.71-85

3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 34 Vol. 9 N.º 2 Junio - Septiembre

http://doi.org/10.17993/3ctecno/2020.v9n2e34.71-85

ABSTRACT

This work presents the newly formulated Dynastic Optimization Algorithm, DOA as applied to the wind

turbine micrositing problem. The data is acquired by the use of the standard MATLAB software at a

wind speed of 12 m/s. The values of the eciency of the algorithm, cost per installation of per unit

turbine, and total dissipated power at each number of turbines installed are discussed.

This algorithm is applied to two test functions and the results are described therein. It has been well-

demonstrated that the proposed DOA exhibits superior performance over GA and DEA for test functions

by hitting the minima very often and with higher precision. On the other hand DOA performance on

WTM problem is also encouraging.

KEYWORDS

Dynastic Optimization Algorithm (DOA), Metaheuristic Algorithms, Genetic Algorithm (GA),

Dierential Evolution Algorithm (DEA), Wind Turbine Micrositing (WTM).

3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 34 Vol. 9 N.º 2 Junio - Septiembre

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1. INTRODUCTION

This work is inspired by the works of Grady, Hussaini, and Abdullah (2005), Mosetti, Poloni, and

Diviacco (1994), Emami and Nougreh (2010) and Marmidis, Lazarou, and Pyrgioti (2008).

The data in this article has been compared with similar results of Mittal (2010), Rajper and Amin

(2012) and Massan, Wagan, & Shaikh (2020). The nature-inspired algorithms use the best combination

and evolution strategy in a given situation. In this work, a new metaheuristic algorithm is developed

by using social behavior in human dynasties. The motivation, conceptual framework, mathematical

model, pseudocode and working of the algorithm are described in this paper and the adjoining papers.

The proposed dynastic optimization algorithm (DOA, which is the base paper supporting this data.

Comparison was also made to similar studies (Massan, Wagan, & Shaikh, 2017; Massan et al., 2015;

Massan et al., 2017a, 2017b).

The eect of wind speed on the resultant power output on an ascending number of turbines arranged

by the metaheuristic method of the Dynastic Optimization Algorithm in a wind farm is evaluated. A

new metaheuristic algorithm for wind form micrositing known as “Dynastic optimization algorithm”

(DOA) was discussed in Massan, Wagan, and Shaikh (2020). The nature-inspired algorithms use the

best combination and evolution strategy in a given situation. In this work, a new metaheuristic algorithm

is developed by using social behavior in human dynasties. The motivation, conceptual framework,

mathematical model, pseudocode and working of the algorithm are described in this paper and the

adjoining papers. The proposed dynastic optimization algorithm (DOA, and the important data about

the power produced, cost per unit turbine installation and eciency of DOA are shared in this data

article. The complete methodology of DOA can be found in Massan, Shaikh, & Wagan (2020). The data

is summarized in Table 1 and Figures 1-3.

3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 34 Vol. 9 N.º 2 Junio - Septiembre

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2. OBJECTIVES

The work describes the data obtained for a novel algorithm that has been presented in Massan, Wagan

and Shaikh (2020). The nature-inspired algorithms use the best combination and evolution strategy

in a given situation. In this work, a new metaheuristic algorithm is developed by using social behavior

in human dynasties. The motivation, conceptual framework, mathematical model, pseudocode and

working of the algorithm are described in this paper and the adjoining papers. The proposed dynastic

optimization algorithm (DOA and puts it forward for wider scientic use. It is evident that it shall prove to

be useful while comparing with other algorithms as applied to this problem and other similar problems.

3. EXPERIMENTAL DESIGN, MATERIALS AND METHODS

The method is described in Massan, Shaikh, and Wagan (2020) and the following parameters have been

used to carry out the simulations.

Using the below dened parameters from Massan, Wagan and Shaikh (2020). The nature-inspired

algorithms use the best combination and evolution strategy in a given situation. In this work, a new

metaheuristic algorithm is developed by using social behavior in human dynasties. The motivation,

conceptual framework, mathematical model, pseudocode and working of the algorithm are described

in this paper and the adjoining papers. The proposed dynastic optimization algorithm (DOA, and

the methodology from Massan, Shaikh, and Wagan (2020), the numerical data concerning the power

produced in (Kwh), cost per unit turbine installation (dimensionless), and the eciency (per unit) of

DOA application is shared in table 1 for the installation of 100 turbines.

3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 34 Vol. 9 N.º 2 Junio - Septiembre

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4. DATA ANALYSIS

The data was acquired by use of a Corei7 laptop (7

generation) and the runtime was less than 8 hours

for Matlab 2017, student version. The data format is raw and analyzed. The parameter values are as per

the given Table 1.

Table 1. Parameters used for DOA implementation.

α = 0.09437,

a = 0.326795,

= 0.88,

= 40m,

= 12m/s, 10 m/s, 8 m/s and 6m/s,

X = 200m

= 0.3,

Z = 60m,

The conguration of DOA being,

Niter, Number of iterations 10,000

Np, Number of population 100

, Ratio of rulers 0.05

, Ratio of workers 0.55

, Ratio of explorers 0.4

rad

, Radius of workers 0.4

The value of the data is that it depicts the actual implementation of a new algorithm for the computation

of the WTM problem. It shall save the computation time for other researchers and shall be a viable

source of comparison of other similar research and application of other algorithms.

This algorithm is competing with other algorithms such as the GA and DEA which are in wide use. The

results are obtained by the use of the same code as used by Mittal (2010) and the data analysis methods

utilized in Sultan, Shaikh, and Chowdhry (2020).

3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 34 Vol. 9 N.º 2 Junio - Septiembre

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The submission of results of a new algorithm in this domain opens new avenues for research and

provides a base for comparison with standard benchmark algorithms. These results shall provide the

basis of scientic testing of the DOA algorithm.

Table 2. Dynastic Optimization Algorithm, Results of power, cost, and efciency per unit turbine.

# of Turbines Power by DOA Cost by DOA Efciency by DOA

1 518.4 0.001927894 1

2 1,036.80 0.001924553 1

3 1,555.20 0.001919021 1

4 2,073.60 0.001911358 1

5 2,592.00 0.001901641 1

6 3,110.40 0.00188997 1

7 3,628.80 0.001876462 1

8 4,147.20 0.00186125 1

9 4,665.60 0.001844484 1

10 5,184.00 0.001826323 1

11 5,702.40 0.001806936 1

12 6,220.80 0.0017865 1

13 6,739.20 0.001765195 1

14 7,257.60 0.001743204 1

15 7,776.00 0.001720706 1

16 8,294.40 0.00169788 1

17 8,812.80 0.001674896 1

18 9,328.22 0.001652447 0.999680735

19 9,845.28 0.00162982 0.999561186

20 10,359.23 0.001607955 0.999153779

21 10,880.17 0.001585428 0.999427594

22 11,394.89 0.001564361 0.999130908

23 11,909.58 0.001543903 0.998857632

24 12,429.13 0.001523553 0.998998052

25 12,805.65 0.00152085 0.988090649

26 13,453.78 0.00148705 0.998173546

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# of Turbines Power by DOA Cost by DOA Efciency by DOA

27 13,969.90 0.001469687 0.998078289

28 14,485.15 0.001453366 0.997929592

29 14,996.40 0.001438399 0.997525317

30 15,514.40 0.00142376 0.997582357

31 16,027.31 0.001410575 0.997318922

32 16,559.21 0.001396744 0.99821631

33 17,053.30 0.001387048 0.996849034

34 17,562.23 0.00137699 0.996404884

35 18,066.46 0.001368154 0.995726221

36 18,573.76 0.001359898 0.995250507

37 19,097.40 0.001351271 0.995652038

38 19,596.40 0.00134515 0.994781272

39 20,131.35 0.0013373 0.995733981

40 20,640.35 0.001331884 0.995387307

41 21,144.41 0.001327386 0.994825064

42 21,664.12 0.001322477 0.995008576

43 22,179.64 0.001318368 0.994995257

44 22,666.38 0.001316417 0.993721187

45 23,181.67 0.001313211 0.993727436

46 23,667.78 0.001312025 0.992509534

47 24,178.36 0.001309801 0.992348055

48 24,685.19 0.001308089 0.992042415

49 25,194.62 0.001306513 0.991851631

50 25,697.39 0.00130552 0.991411503

51 26,203.16 0.001304578 0.991102259

52 26,719.00 0.001303325 0.991178533

53 27,210.82 0.001303398 0.99037745

54 27,748.88 0.001301409 0.991258057

55 28,193.69 0.001303894 0.988835927

56 28,753.09 0.001301182 0.990447563

57 29,130.48 0.001306762 0.985843065

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# of Turbines Power by DOA Cost by DOA Efciency by DOA

58 29,687.59 0.001304321 0.987374528

59 30,242.16 0.001302135 0.988771037

60 30,741.34 0.001302418 0.988340485

61 31,278.57 0.001301147 0.989126935

62 31,640.64 0.00130715 0.984438589

63 32,200.11 0.001304997 0.985943057

64 32,642.62 0.00130761 0.98387515

65 33,123.50 0.001308655 0.983009914

66 33,632.55 0.001308591 0.982994074

67 34,173.13 0.001307335 0.983886443

68 34,195.85 0.001325909 0.970061967

69 35,102.20 0.001310625 0.981341563

70 35,651.06 0.001309114 0.982447598

71 36,224.84 0.001306755 0.984199447

72 36,637.20 0.001310223 0.981577858

73 37,072.03 0.001312822 0.979621874

74 37,613.83 0.001311622 0.980507256

75 38,080.59 0.001313042 0.979439083

76 38,671.75 0.001310201 0.981556231

77 39,084.93 0.001313401 0.979159875

78 39,661.54 0.00131111 0.98086661

79 39,516.82 0.001332779 0.964916909

80 40,750.09 0.0013088 0.982592726

81 41,107.04 0.001313651 0.97896282

82 41,465.55 0.001318369 0.975458058

83 42,185.95 0.001311657 0.980448512

84 42,506.64 0.001317444 0.976140856

85 43,123.26 0.001314065 0.978650658

86 43,316.21 0.001323602 0.971598857

87 43,863.89 0.001322274 0.972574453

88 44,328.75 0.001323446 0.971712521

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# of Turbines Power by DOA Cost by DOA Efciency by DOA

89 44,977.38 0.001319182 0.974852994

90 45,593.26 0.001315985 0.977221701

91 45,646.31 0.00132906 0.967607595

92 46,039.29 0.001332196 0.965330019

93 46,885.14 0.001322381 0.972494843

94 47,024.66 0.001332634 0.965012274

95 47,563.55 0.001331552 0.965796586

96 48,202.02 0.001327745 0.968565566

97 48,753.12 0.001326411 0.969539892

98 48,430.18 0.001349021 0.953290011

99 49,256.42 0.001339927 0.959759948

100 49,831.45 0.001337843 0.961254806

Figure 1. Comparison of mean power (kWh) produced by DEA (Massan et al., 2017a, 2017b), DOA

(Massan, Wagan, & Shaikh, 2020) and GA (Rajper & Amin, 2012) versus number of turbines.

Figure 2. Comparison of mean cost per unit turbine (dimensionless) by DEA (Massan et al., 2017a, 2017b),

DOA (Massan, Wagan, & Shaikh, 2020) and GA (Rajper & Amin, 2012) versus number of turbines.

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

1 to 10 11 to 20 21 to 30 31 to 40 41 to 50 51 to 60 61 to 70 71 to 80 81 to 90 91 to 100

Differential Evolution Algorithm Dynastic Optimization Algortihm Genetic Algorthm

0,0002

0,0004

0,0006

0,0008

0,001

0,0012

0,0014

0,0016

0,0018

0,002

1 to 10 11 to 20 21 to 30 31 to 40 41 to 50 51 to 60 61 to 70 71 to 80 81 to 90 91 to 100

Differential Evolution Algorithm Dynastic Optimization Algortihm Genetic Algorthm

Figure 1. Comparison of mean power (kWh) produced by DEA (Massan et al., 2017a, 2017b), DOA (Massan, Wagan, & Shaikh,

2020). The nature-inspired algorithms use the best combination and evolution strategy in a given situation. In this work, a new

metaheuristic algorithm is developed by using social behavior in human dynasties. The motivation, conceptual framework,

mathematical model, pseudocode and working of the algorithm are described in this paper and the adjoining papers. The proposed

dynastic optimization algorithm (DOA and GA (Rajper & Amin, 2012) versus number of turbines.

3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 34 Vol. 9 N.º 2 Junio - Septiembre

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Figure 1. Comparison of mean power (kWh) produced by DEA (Massan et al., 2017a, 2017b), DOA

(Massan, Wagan, & Shaikh, 2020) and GA (Rajper & Amin, 2012) versus number of turbines.

Figure 2. Comparison of mean cost per unit turbine (dimensionless) by DEA (Massan et al., 2017a, 2017b),

DOA (Massan, Wagan, & Shaikh, 2020) and GA (Rajper & Amin, 2012) versus number of turbines.

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

1 to 10 11 to 20 21 to 30 31 to 40 41 to 50 51 to 60 61 to 70 71 to 80 81 to 90 91 to 100

Differential Evolution Algorithm Dynastic Optimization Algortihm Genetic Algorthm

0,0002

0,0004

0,0006

0,0008

0,001

0,0012

0,0014

0,0016

0,0018

0,002

1 to 10 11 to 20 21 to 30 31 to 40 41 to 50 51 to 60 61 to 70 71 to 80 81 to 90 91 to 100

Differential Evolution Algorithm Dynastic Optimization Algortihm Genetic Algorthm

Figure 2. Comparison of mean cost per unit turbine (dimensionless) by DEA (Massan et al., 2017a, 2017b), DOA (Massan,

Wagan, & Shaikh, 2020). The nature-inspired algorithms use the best combination and evolution strategy in a given situation. In

this work, a new metaheuristic algorithm is developed by using social behavior in human dynasties. The motivation, conceptual

framework, mathematical model, pseudocode and working of the algorithm are described in this paper and the adjoining papers.

The proposed dynastic optimization algorithm (DOA and GA (Rajper & Amin, 2012) versus number of turbines.

Figure 3. Comparison of efficiencies (per unit) by DEA (Massan et al., 2017a, 2017b), DOA (Massan,

Wagan, & Shaikh, 2020) and GA (Rajper & Amin, 2012) versus number of turbines.

5. Test functions

This algorithm was applied to the following two test functions and the comparative

graphs are obtained herewith,

The DOA, DEA and GA were applied to the following test functions,

1) Booths’s (f

) and



(



, 

)

= (

+ 2

− 7)

+ (2

+ 

− 5)



2) the Bohachevsky’s (f2) functions



(



, 

)

= −

+ 2

− 0.3 cos

(

3

)

− 0.4 cos

(

4

)

+ 0.7

The following figures were obtained,

0,2

0,4

0,6

0,8

1,2

1 to 10 11 to 20 21 to 30 31 to 40 41 to 50 51 to 60 61 to 70 71 to 80 81 to 90 91 to 100

Differential Evolution Algorithm Dynastic Optimization Algortihm Genetic Algorthm (not available)

Figure 3. Comparison of efciencies (per unit) by DEA (Massan et al., 2017a, 2017b), DOA (Massan, Wagan, & Shaikh, 2020). The

nature-inspired algorithms use the best combination and evolution strategy in a given situation. In this work, a new metaheuristic

algorithm is developed by using social behavior in human dynasties. The motivation, conceptual framework, mathematical model,

pseudocode and working of the algorithm are described in this paper and the adjoining papers. The proposed dynastic optimization

algorithm (DOA and GA (Rajper & Amin, 2012) versus number of turbines.

3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 34 Vol. 9 N.º 2 Junio - Septiembre

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5. TEST FUNCTIONS

This algorithm was applied to the following two test functions and the comparative graphs are obtained

herewith,

The DOA, DEA and GA were applied to the following test functions,

Booths’s (f

) and

Figure 3. Comparison of efficiencies (per unit) by DEA (Massan et al., 2017a, 2017b), DOA (Massan,

Wagan, & Shaikh, 2020) and GA (Rajper & Amin, 2012) versus number of turbines.

5. Test functions

This algorithm was applied to the following two test functions and the comparative

graphs are obtained herewith,

The DOA, DEA and GA were applied to the following test functions,

1) Booths’s (f

) and



(



, 

)

= (

+ 2

− 7)

+ (2

+ 

− 5)



2) the Bohachevsky’s (f2) functions



(



, 

)

= −

+ 2

− 0.3 cos

(

3

)

− 0.4 cos

(

4

)

+ 0.7

The following figures were obtained,

0,2

0,4

0,6

0,8

1,2

1 to 10 11 to 20 21 to 30 31 to 40 41 to 50 51 to 60 61 to 70 71 to 80 81 to 90 91 to 100

Differential Evolution Algorithm Dynastic Optimization Algortihm Genetic Algorthm (not available)

the Bohachevsky’s (f2) functions

Figure 3. Comparison of efficiencies (per unit) by DEA (Massan et al., 2017a, 2017b), DOA (Massan,

Wagan, & Shaikh, 2020) and GA (Rajper & Amin, 2012) versus number of turbines.

5. Test functions

This algorithm was applied to the following two test functions and the comparative

graphs are obtained herewith,

The DOA, DEA and GA were applied to the following test functions,

1) Booths’s (f

) and



(



, 

)

= (

+ 2

− 7)

+ (2

+ 

− 5)



2) the Bohachevsky’s (f2) functions



(



, 

)

= −

+ 2

− 0.3 cos

(

3

)

− 0.4 cos

(

4

)

+ 0.7

The following figures were obtained,

0,2

0,4

0,6

0,8

1,2

1 to 10 11 to 20 21 to 30 31 to 40 41 to 50 51 to 60 61 to 70 71 to 80 81 to 90 91 to 100

Differential Evolution Algorithm Dynastic Optimization Algortihm Genetic Algorthm (not available)

The following gures were obtained,

Figure 4. Comparison of minima attained versus number of generations by all methods for Booth’s function.

3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 34 Vol. 9 N.º 2 Junio - Septiembre

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Figure 5. Comparison of minima attained versus number of generations by all methods for Bohachevsky’s function.

The minimum value of the Booth’s function is 0 at (1,3) and the minimum value of the Bohachevsky’s

function is 0 at (0,0).

The DOA approaches the minima of f1 and f2 more frequently and with comparatively much higher

precision than GA and DEA as demonstrated through Figures 4 and 5 for a several values of generations.

6. RECOMMENDATIONS

In view of the encouraging results of the DOA algorithm it is now possible to depict that it is a viable

algorithm that may be used in dierent elds of technology. The values of the test functions also depict

encouraging results for this algorithm.

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7. CONCLUSION

The potential power saving, cost saving and eciency benets of proposed DOA (Massan, Wagan, and

Shaikh, 2020). The nature-inspired algorithms use the best combination and evolution strategy in a given

situation. In this work, a new metaheuristic algorithm is developed by using social behavior in human

dynasties. The motivation, conceptual framework, mathematical model, pseudocode and working of

the algorithm are described in this paper and the adjoining papers. The proposed dynastic optimization

algorithm (DOA are shown in Figures 1-3, respectively against Dierential Evolution Algorithm (Massan

et al., 2017a, 2017b) and genetic algorithm data (Rajper & Amin, 2012). The encouraging performance

of DOA over GA and DEA is evident from the exhaustive comparison in Massan, Wagan, and Shaikh

(2020). The nature-inspired algorithms use the best combination and evolution strategy in a given

situation. In this work, a new metaheuristic algorithm is developed by using social behavior in human

dynasties. The motivation, conceptual framework, mathematical model, pseudocode and working of

the algorithm are described in this paper and the adjoining papers. The proposed dynastic optimization

algorithm (DOA and the data shared in this article.

ACKNOWLEDGEMENT

The authors wish to thank Hazrat Manzoor Hussain (RA) for his guidance and support.

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