International Journal of Advances in Applied Sciences (IJAAS) Volume 10, issue 2, Jun. 2021

ISSN: 2252-8814

International Journal of

Advances in Applied Sciences

IJAAS

Editor-in-Chief Qing Wang, Shandong University of Science and Technology, China

Managing Editors Chen-Yuan Chen, National Pingtung University of Education, Taiwan Guangming Yao, Harbin Normal University, China Habibolla Latifizadeh, West Virginia University, United States Md. Shakhaoath Khan, RMIT University, Australia Mohammad Hossein Ahmadi, Shahrood University of Technology, Iran Tole Sutikno, Universitas Ahmad Dahlan, Indonesia

Associate Editors: A. Ozan Bicen, Sabanci University, Turkey Abdalhossein Rezai, Isfahan University of Technology, Iran Abdul Sattar Dogonchi, Babol Noshirvani University of Technology, Iran Abdullah Al-Hadi Azremi, University Malaysia Perlis, Malaysia Adam M. Kawalec, Military University of Technology, Poland Agrawal Rajeev, G L Bajaj Institute of Technology & Management, India Ahmad Badrul Hisham, Universiti Teknikal Malaysia Melaka, Malaysia Ahmad Rifqi Md Zain, Institute of Microengineering and Nanoelectronics, Malaysia Ali Mohammad Saghiri, Amirkabir University of Technology, Iran Amir Khalid, Universiti Tun Hussein Onn Malaysia, Malaysia Anna Guerra, University of Bologna, Italy Arcangelo Castiglione, Università degli Studi di Salerno, Italy Arun Sharma, Indira Gandhi Delhi Technical University for Women, India Ayan Mondal, Indian Institute of Technology, India Bakaul Masuduzzaman, Diodar Ltd, Australia Bibhudatta Sahoo, National Institute of Technology, India Brij Bhooshan Gupta, National Institute of Technology, India

Carlos Becker Westphall, Federal University of Santa Catarina, Brazil Dakshina Ranjan Kisku, National Institute of Technology, India Ezra Morris, Universiti Tunku Abdul Rahman, Malaysia Félix J. García Clemente, University of Murcia, Spain Florian Kongoli, Flogen Technologies Inc., Canada Grienggrai Rajchakit, Maejo University, Thailand Haikal El Abed, Technical Trainers College, Saudi Arabia Ibrahim Hamidah D., Universiti Putra Malaysia, Malaysia Imran Shafique Ansari, University of Glasgow, United Kingdom Inderpreet Kaur, Guru Nanak Dev Engineering College Ludhiana, India Ismail Idris, Universiti Teknologi Petronas, Malaysia Jitendra K. Madaan, Indian Institute of Technology Delhi, India Joao Weyl Costa, Universidade Federal do Pará, Brazil Kang Song, Qingdao University, China Ke-Lin Du, Concordia University, Canada Larbi Boubchir, University of Paris 8, France Ligang Zhang, Central Queensland University, Australia M. A. Jabbar, Jawaharlal Nehru Technological University, India M. EL-Shimy, Ain Shams University, Egypt (Continued on the next page)

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Mahdi Imani, George Washington University, United States Makram A. Fakhry, University of Technology, Iraq Marco Carratù, University of Salerno, Italy Marco Listanti, University of Rome "La Sapienza", Italy Mayank Dave, National Intitute of Technology Kurukshetra, India Md. Shohel Sayeed, Multimedia University, Malaysia Mohammad Alibakhshikenari, Università degli Studi di Roma "Tor Vergata", Italy Mohd Ashraf Ahmad, Universiti Malaysia Pahang, Malaysia Mohd Khair Hassan, Universiti Putra Malaysia, Malaysia Mojallali Hamed, University of Guilan, Iran N. Ramesh Babu, M. Kumarasamy College of Engineering, India Naser Ojaroudi Parchin, University of Bradford, United Kingdom Nicola Ivan Giannoccaro, University of Salento, Italy Norizam Sulaiman, Universiti Malaysia Pahang, Malaysia Nuno Rodrigues, Instituto Politécnico de Bragança, Portugal Orhan Ekren, Ege University Solar Energy Institute, Turkey Otávio Noura Teixeira, Universidade Federal do Para, Brazil Panić Stefan, Tomsk Polytechnic University, Serbia Paolo Crippa, Università Politecnica delle Marche, Italy Pascal Lorenz, University of Haute Alsace, France

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IJAAS

International Journal of

Advances in Applied Sciences

Factual power loss reduction by dynamic membrane evolutionary algorithm Lenin Kanagabasai

99

iPark: automated smart parking system Rahman Atiqur

107

Confirmatory factor analysis: Model testing of financial ratio's with decision support systems approach T. Husain, Maulana Ardhiansyah, Dedin Fathudin

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A numerical algorithm to find a root of non-linearequations using householder’s method Srinivasarao Thota

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Real power loss diminution by rain drop optimization algorithm Lenin Kanagasabai

149

Groundwater suitability for irrigated agriculture in Alluvial Bengal delta plain: A review Md. Shajedul Islam, M. G. Mostafa

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Design and implementation of an African native language-based programming language Ezekiel Kolawole Olatunji, John. B. Oladosu, Odetunji A. Odejobi, Stephen O. Olabiyisi

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188

Responsibility of the contents rest upon the authors and not upon the publisher or editor

IJAAS

Vol. 10

No. 2

pp. 99 - 192

June 2021

ISSN 2252-8814

International Journal of Advances in Applied Sciences (IJAAS) Vol. 10, No. 2, June 2021, pp. 99~106 ISSN: 2252-8814, DOI: 10.11591/ijaas.v10.i2.pp99-106

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99

Factual power loss reduction by dynamic membrane evolutionary algorithm Lenin Kanagabasai Department of EEE, Prasad V. Potluri Siddhartha Institute of Technology, Kanuru, Vijayawada, Andhra Pradesh, India

Article Info

ABSTRACT

Article history:

This paper presents Dynamic Membrane Evolutionary Algorithm (DMEA) has been applied to solve optimal reactive power problem. Proposed methodology merges the fusion and division rules of P systems with active membranes and with adaptive differential evolution (ADE), particle swarm optimization (PSO) exploration stratagem. All elementary membranes are amalgamated into one membrane in the computing procedure. Furthermore, integrated membrane are alienated into the elementary membranes 1, 2,_ m.

In particle swarm optimization (PSO) 𝑪𝟏 , 𝑪𝟐 (acceleration constants) are vital parameters to augment the exploration ability of PSO in the period of the optimization procedure. In this work, Gaussian probability distribution is initiated to engender the accelerating coefficients of PSO. Proposed Dynamic Membrane Evolutionary Algorithm (DMEA) has been tested in standard IEEE 14, 30, 57,118,300 bus test systems and simulation results show the projected algorithm reduced the real power loss comprehensively.

Received Apr 4, 2020 Revised Dec 1, 2020 Accepted Feb 22, 2021 Keywords: Dynamic membrane evolutionary algorithm Optimal reactive power Transmission loss

This is an open access article under the CC BY-SA license.

Corresponding Author: Lenin Kanagasabai Department of EEE Prasad V. Potluri Siddhartha Institute of Technology Kanuru, Vijayawada, Andhra Pradesh-520007, India Email: gklenin@gmail.com

1.

INTRODUCTION Reactive power problem plays a key role in secure and economic operations of power system.

Optimal reactive power problem has been solved by variety of types of methods [1]-[6]. Nevertheless numerous scientific difficulties are found while solving problem due to an assortment of constraints.

Evolutionary techniques [7]-[16] are applied to solve the reactive power problem, but the main problem is many algorithms get stuck in local optimal solution & failed to balance the Exploration & Exploitation during the search of global solution. In this paper, Dynamic Membrane Evolutionary Algorithm (DMEA) has been applied to solve optimal reactive power problem. Proposed methodology merges the fusion and division rules of P systems with active membranes and with adaptive differential evolution (ADE), particle swarm optimization (PSO) exploration stratagem. In this work, composition of the dynamic membrane algorithm along with the fusion, division rules are utilized to solve the optimal reactive power problem. In skin membrane 0, elementary membranes 1, 2,_, m are embedded in the structure and it contains set of evolutionary, communication rules, multi-set of objects . All elementary membranes are amalgamated into one membrane in the computing procedure. Furthermore, integrated membrane are alienated into the elementary membranes 1, 2,_, m. In particle swarm optimization (PSO), 𝐶1 , 𝐶2 (acceleration constants) are vital parameters to augment the exploration ability of PSO in the period of the optimization procedure.

Conversely, dissimilar optimization problems has altered values for the acceleration constants, it will not be Journal homepage: http://ijaas.iaescore.com

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an effortless assignment to choose the optimal values. In this work, Gaussian probability distribution is initiated to engender the accelerating coefficients of PSO. Particle swarm optimization (PSO) based on Gaussian distribution will be employed concurrently in area from 1 to m. The Proposed Dynamic Membrane Evolutionary Algorithm (DMEA) has been tested in standard IEEE 14, 30, 57,118,300 bus test system and simulation results show the projected algorithm reduced the real power loss extensively.

2.

PROBLEM FORMULATION Objective of the problem is to reduce the true power loss as (1).

F= PL = ∑k∈Nbr g k (Vi2 + Vj2 − 2Vi Vj cosθij )

(1)

Voltage deviation given as (2).

F = PL + ωv × Voltage Deviatio

(2)

Voltage deviation given by (3).

Npq

Voltage Deviation = ∑i=1 |Vi − 1|

(3)

Constraint (Equality).

PG = PD + PL

(4)

Constraints (Inequality). max min Pgslack ≤ Pgslack ≤ Pgslack

(5)

max Qmin gi ≤ Q gi ≤ Q gi , i ∈ Ng

(6)

Vimin ≤ Vi ≤ Vimax , i ∈ N

(7)

Timin ≤ Ti ≤ Timax , i ∈ NT

(8)

Qmin ≤ Q c ≤ Qmax , i ∈ NC c C

(9)

3.

DYNAMIC MEMBRANE EVOLUTIONARY ALGORITHM In membrane computing, P systems with dynamic membranes are a very blistering research topic and the analogous membrane algorithms have been used extensively to solve various types of optimization problems [17]. In this work, composition of the dynamic membrane algorithm along with the fusion, division rules are utilized to solve the optimal reactive power problem. In skin membrane 0, elementary membranes 1, 2,_, m are embedded in the structure and it contains set of evolutionary, communication rules, multi-set of objects. All elementary membranes are amalgamated into one membrane in the computing procedure.

Furthermore, integrated membrane are alienated into the elementary membranes 1, 2,.., m. Proposed methodology merges the fusion and division rules of P systems with active membranes and with adaptive differential evolution (ADE), particle swarm optimization (PSO) exploration stratagem. a. One level membrane structure has been specified b. In particle swarm optimization (PSO), 𝐶1 , 𝐶2 (acceleration constants) are vital parameters to augment the exploration ability of PSO in the period of the optimization procedure. Conversely, dissimilar optimization problems has altered values for the acceleration constants, it will not be an effortless assignment to choose the optimal values. In this work, Gaussian probability distribution is initiated to engender the accelerating coefficients of PSO. Particle swarm optimization (PSO) based on Gaussian distribution will be employed concurrently in area from 1 to m. − Start − Position and velocity are initialized − Compute the fitness value − Pbest and Gbest are updated Int J Adv Appl Sci, Vol. 10, No. 2, June 2021: 99 – 106

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− If stop criterion satisfied then end or else update Position and velocity go to step iii − End 𝑘+1 𝑘 𝑘 𝑘 𝑘 𝑣𝑖,𝑗 = |𝑟𝑎𝑛𝑑𝑜𝑚𝑛( )| × (𝑃𝑏𝑒𝑠𝑡𝑖,𝑗 − 𝑥𝑖,𝑗 ) + |𝑟𝑎𝑛𝑑𝑜𝑚𝑛( )| × (𝐺𝑏𝑒𝑠𝑡𝑖,𝑗 − 𝑥𝑖,𝑗 )

(10)

𝑘+1 𝑘 𝑘+1 𝑥𝑖,𝑗 = 𝑥𝑖,𝑗 + 𝑣𝑖,𝑗

(11)

c. Execute the integration process, all elementary membranes are amalgamated into one elementary membrane one 𝑚𝑜𝑛𝑒 and all elementary membranes strings are go into the membrane 𝑚𝑜𝑛𝑒 . d. In mone membrane, adaptive differential evolution is utilized to modernize the strings object. In this work self-adaptive method is used to control the parameters CR and F. 𝐶𝑅𝑖 (𝑡) = 𝐶𝑅𝑖1 (𝑡) + 𝑁(0,1) × (𝐶𝑅𝑖2 (𝑡) − 𝐶𝑅𝑖3 (𝑡))

(12)

𝐹𝑖 (𝑡) = 𝐹𝑖4 (𝑡) + 𝑁(0,0.5) × (𝐹𝑖5 (𝑡) − 𝐹𝑖6 (𝑡))

(13)

− Engender the preliminary population − For each individual in the population ; Engender three arbitrary different integers r1 , r2 and r3 ∈ {1,2, . . , N} and Engender an arbitrary integer Jrandom ∈ {1,2, . , n} ′ − If randomJ (0,1) < CR then xi,j = xi,r3 + F ∗ (xi,r1 − xi,r2 ) ′ − Else xi,j = xi,j − End if − End for − If Fitenss(xi′ ) ≤ Fitness(xi ) ; then xi = xi′ − End if − End for − End condition ′ When 𝑥𝑖,𝑗 infringe the boundary constraint, and then the violated variable value is brought back by, ′ 𝑥𝑚𝑖𝑛,𝑗 𝑖𝑓( 𝑟𝑎𝑛𝑑𝑜𝑚 ( ) ≤ 0.5)˅(𝑥𝑖,𝑗 < 𝑥𝑚𝑖𝑛𝑖𝑚𝑢𝑚,𝑗 ) ′ 𝑥𝑖,𝑗 =

′ 𝑥𝑚𝑎𝑥,𝑗 𝑖𝑓( 𝑟𝑎𝑛𝑑𝑜𝑚 ( ) ≤ 0.5)˅(𝑥𝑖,𝑗 < 𝑥𝑚𝑎𝑥𝑖𝑚𝑢𝑚,𝑗 ) ′ ′ 2 × 𝑥𝑚𝑖𝑛,𝑗 − 𝑥𝑖,𝑗 𝑖𝑓( 𝑟𝑎𝑛𝑑𝑜𝑚 ( ) > 0.5)˅(𝑥𝑖,𝑗 < 𝑥𝑚𝑖𝑛𝑖𝑚𝑢𝑚,𝑗 )

(14)

′ ′ {2 × 𝑥𝑚𝑖𝑛,𝑗 − 𝑥𝑖,𝑗 𝑖𝑓( 𝑟𝑎𝑛𝑑𝑜𝑚 ( ) > 0.5)˅(𝑥𝑖,𝑗 < 𝑥𝑚𝑎𝑥𝑖𝑚𝑢𝑚,𝑗 )

e. By using fitness function compute the fitness of each string f. Employ the contact rules, a replica of the most excellent strings are chosen in the membrane mone which will be sent to the skin membrane, and the present most excellent strings are accumulated in the skin membrane. g. Once the end condition is met, subsequently output the results; otherwise go to Step h. h. With the m elementary membranes mone Membrane is alienated into the identical structure. At present most excellent strings and 𝑁𝑠 − 1strings with the poor fitness will be send to every elementary membrane in roll by the send-in contact rules, and then go back to Step b. i. End condition is the utmost number of iterations. Algorithm will end if the utmost number of iterations is reached, and output the results.

4.

SIMULATION RESULTS At first in standard IEEE 14 bus system the validity of the proposed Dynamic Membrane Evolutionary Algorithm (DMEA) has been tested, Table 1 shows the constraints of control variables Table 2 shows the limits of reactive power generators and comparison results are presented in Table 3.

Table 1. Constraints of control variables System IEEE 14 Bus

Variables Generator Voltage Transformer Tap VAR Source

Minimum (PU) 0.95 o.9 0

Maximum (PU) 1.1 1.1 0.20

Factual power loss reduction by dynamic membrane evolutionary algorithm (Lenin Kanagabasai)

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ISSN: 2252-8814 Table 2. Constrains of reactive power generators System IEEE 14 Bus

Variables 1 2 3 6 8

Q Minimum (PU) 0 -40 0 -6 -6

Q Maximum (PU) 10 50 40 24 24

Table 3. Simulation results of IEEE −14 system Control variables 𝑉𝐺−1 𝑉𝐺−2 𝑉𝐺−3 𝑉𝐺−6 𝑉𝐺−8 𝑇𝑎𝑝 8 𝑇𝑎𝑝 9 𝑇𝑎𝑝 10 𝑄𝐶−9 𝑃𝐺 𝑄𝐺 (Mvar) Reduction in PLoss (%) Total PLoss (Mw) NR* - Not reported.

Base case 1.060 1.045 1.010 1.070 1.090 0.978 0.969 0.932 0.19 272.39 82.44 0 13.550

MPSO [18] 1.100 1.085 1.055 1.069 1.074 1.018 0.975 1.024 14.64 271.32 75.79 9.2 12.293

PSO [18] 1.100 1.086 1.056 1.067 1.060 1.019 0.988 1.008 0.185 271.32 76.79 9.1 12.315

EP [18] NR* 1.029 1.016 1.097 1.053 1.04 0.94 1.03 0.18 NR* NR* 1.5 13.346

SARGA [18] NR* 1.060 1.036 1.099 1.078 0.95 0.95 0.96 0.06 NR* NR* 2.5 13.216

DMEA 1.020 1.041 1.052 1.060 1.024 0.961 0.952 0.908 0.162 271.02 74.98 18.095 11.098

Then the proposed Dynamic Membrane Evolutionary Algorithm (DMEA) has been tested, in IEEE 30 Bus system. Table 4 shows the constraints of control variables, Table 5 shows the limits of reactive power generators and comparison results are presented in Table 6.

Then the proposed Dynamic Membrane Evolutionary Algorithm (DMEA) has been tested, in IEEE 57 Bus system. Table 7 shows the constraints of control variables, Table 8 shows the limits of reactive power generators and comparison results are presented in Table 9.

Then the proposed Dynamic Membrane Evolutionary Algorithm (DMEA) has been tested, in IEEE 118 Bus system. Table 10 shows the constraints of control variables and comparison results are presented in Table 11.

Then IEEE 300 bus system [19] is used as test system to validate the performance of the Dynamic Membrane Evolutionary Algorithm (DMEA). Table 12 shows the comparison of real power loss obtained after optimization.

Table 4. Constraints of control variables System IEEE 30 Bus

Variables Generator Voltage Transformer Tap VAR Source

Minimum (PU) 0.95 o.9 0

Maximum (PU) 1.1 1.1 0.20

Table 5. Constrains of reactive power generators System IEEE 30 Bus

Variables 1 2 5 8 11 13

Q Minimum (PU) 0 -40 -40 -10 -6 -6

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Q Maximum (PU) 10 50 40 40 24 24

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Table 6. Simulation results of IEEE −30 system Control variables 𝑉𝐺−1 𝑉𝐺−2 𝑉𝐺−5 𝑉𝐺−8 𝑉𝐺−12 VG-13 Tap11 Tap12 Tap15 Tap36 QC10 QC24 𝑃𝐺 (MW) 𝑄𝐺 (Mvar) Reduction in PLoss (%) Total PLoss (Mw) NR* - Not reported.

Base case 1.060 1.045 1.010 1.010 1.082 1.071 0.978 0.969 0.932 0.968 0.19 0.043 300.9 133.9 0 17.55

MPSO [18] 1.101 1.086 1.047 1.057 1.048 1.068 0.983 1.023 1.020 0.988 0.077 0.119 299.54 130.83 8.4 16.07

PSO [18] 1.100 1.072 1.038 1.048 1.058 1.080 0.987 1.015 1.020 1.012 0.077 0.128 299.54 130.94 7.4 16.25

EP [18] NR* 1.097 1.049 1.033 1.092 1.091 1.01 1.03 1.07 0.99 0.19 0.04 NR* NR* 6.6 16.38

SARGA [18] NR* 1.094 1.053 1.059 1.099 1.099 0.99 1.03 0.98 0.96 0.19 0.04 NR* NR* 8.3 16.09

DMEA 1.010 1.032 1.042 1.026 1.068 1.080 0.934 0.946 0.920 0.916 0.079 0.126 298.32 130.04 12.13 15.42

Table 7. Constraints of control variables System IEEE 57 Bus

Variables Generator Voltage Transformer Tap VAR Source

Minimum (PU) 0.95 o.9 0

Maximum (PU) 1.1 1.1 0.20

Table 8. Constrains of reactive power generators System IEEE 57 Bus

Variables 1 2 3 6 8 9 12

Q Minimum (PU) -140 -17 -10 -8 -140 -3 -150

Q Maximum (PU) 200 50 60 25 200 9 155

Table 9. Simulation results of IEEE −57 system Control variables 𝑉𝐺 1 𝑉𝐺 2 𝑉𝐺 3 𝑉𝐺 6 𝑉𝐺 8 𝑉𝐺 9 𝑉𝐺 12 𝑇𝑎𝑝 19 𝑇𝑎𝑝 20 𝑇𝑎𝑝 31 𝑇𝑎𝑝 35 𝑇𝑎𝑝 36 𝑇𝑎𝑝 37 𝑇𝑎𝑝 41 𝑇𝑎𝑝 46 𝑇𝑎𝑝 54 𝑇𝑎𝑝 58 𝑇𝑎𝑝 59 𝑇𝑎𝑝 65 𝑇𝑎𝑝 66 𝑇𝑎𝑝 71 𝑇𝑎𝑝 73 𝑇𝑎𝑝 76 𝑇𝑎𝑝 80 𝑄𝐶 18 𝑄𝐶 25 𝑄𝐶 53 𝑃𝐺 (MW) 𝑄𝐺 (Mvar) Reduction in PLoss (%) Total PLoss (Mw) NR* - Not reported.

Base case 1.040 1.010 0.985 0.980 1.005 0.980 1.015 0.970 0.978 1.043 1.000 1.000 1.043 0.967 0.975 0.955 0.955 0.900 0.930 0.895 0.958 0.958 0.980 0.940 0.1 0.059 0.063 1278.6 321.08 0 27.8

MPSO [18] 1.093 1.086 1.056 1.038 1.066 1.054 1.054 0.975 0.982 0.975 1.025 1.002 1.007 0.994 1.013 0.988 0.979 0.983 1.015 0.975 1.020 1.001 0.979 1.002 0.179 0.176 0.141 1274.4 272.27 15.4 23.51

PSO [18] 1.083 1.071 1.055 1.036 1.059 1.048 1.046 0.987 0.983 0.981 1.003 0.985 1.009 1.007 1.018 0.986 0.992 0.990 0.997 0.984 0.990 0.988 0.980 1.017 0.131 0.144 0.162 1274.8 276.58 14.1 23.86

CGA [18] 0.968 1.049 1.056 0.987 1.022 0.991 1.004 0.920 0.920 0.970 NR* NR* 0.900 0.910 1.100 0.940 0.950 1.030 1.090 0.900 0.900 1.000 0.960 1.000 0.084 0.008 0.053 1276 309.1 9.2 25.24

AGA [18] 1.027 1.011 1.033 1.001 1.051 1.051 1.057 1.030 1.020 1.060 NR* NR* 0.990 1.100 0.980 1.010 1.080 0.940 0.950 1.050 0.950 1.010 0.940 1.000 0.016 0.015 0.038 1275 304.4 11.6 24.56

DMEA 1.021 1.048 1.031 1.030 1.048 1.026 1.060 0.962 0.946 0.969 1.012 1.000 1.003 0.990 1.010 0.980 0.964 0.979 1.010 0.972 1.019 1.000 0.973 1.000 0.171 0.170 0.140 1269.1 269.26 20.72 22.04

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ISSN: 2252-8814 Table 10. Constraints of control variables System IEEE 118 Bus

Variables Generator Voltage Transformer Tap VAR Source

Minimum (PU) 0.95 o.9 0

Maximum (PU) 1.1 1.1 0.20

Table 11. Simulation results of IEEE −118 system Control variables 𝑉𝐺 1 𝑉𝐺 4 𝑉𝐺 6 𝑉𝐺 8 𝑉𝐺 10 𝑉𝐺 12 𝑉𝐺 15 𝑉𝐺 18 𝑉𝐺 19 𝑉𝐺 24 𝑉𝐺 25 𝑉𝐺 26 𝑉𝐺 27 𝑉𝐺31 𝑉𝐺 32 𝑉𝐺 34 𝑉𝐺 36 𝑉𝐺 40 𝑉𝐺 42 𝑉𝐺 46 𝑉𝐺 49 𝑉𝐺 54 𝑉𝐺 55 𝑉𝐺56 𝑉𝐺 59 𝑉𝐺 61 𝑉𝐺 62 𝑉𝐺 65 𝑉𝐺 66 𝑉𝐺 69 𝑉𝐺 70 𝑉𝐺 72 𝑉𝐺 73 𝑉𝐺 74 𝑉𝐺 76 𝑉𝐺 77 𝑉𝐺 80 𝑉𝐺 85 𝑉𝐺 87 𝑉𝐺 89 𝑉𝐺 90 𝑉𝐺 91 𝑉𝐺 92 𝑉𝐺 99 𝑉𝐺 100 𝑉𝐺 103 𝑉𝐺 104 𝑉𝐺 105 𝑉𝐺 107 𝑉𝐺 110 𝑉𝐺 111 𝑉𝐺 112 𝑉𝐺 113 𝑉𝐺 116 𝑇𝑎𝑝 8 𝑇𝑎𝑝 32 𝑇𝑎𝑝 36 𝑇𝑎𝑝 51 𝑇𝑎𝑝 93 𝑇𝑎𝑝 95 𝑇𝑎𝑝 102 𝑇𝑎𝑝 107

Base case 0.955 0.998 0.990 1.015 1.050 0.990 0.970 0.973 0.962 0.992 1.050 1.015 0.968 0.967 0.963 0.984 0.980 0.970 0.985 1.005 1.025 0.955 0.952 0.954 0.985 0.995 0.998 1.005 1.050 1.035 0.984 0.980 0.991 0.958 0.943 1.006 1.040 0.985 1.015 1.000 1.005 0.980 0.990 1.010 1.017 1.010 0.971 0.965 0.952 0.973 0.980 0.975 0.993 1.005 0.985 0.960 0.960 0.935 0.960 0.985 0.935 0.935

MPSO [18] 1.021 1.044 1.044 1.063 1.084 1.032 1.024 1.042 1.031 1.058 1.064 1.033 1.020 1.023 1.023 1.034 1.035 1.016 1.019 1.010 1.045 1.029 1.031 1.029 1.052 1.042 1.029 1.054 1.056 1.072 1.040 1.039 1.028 1.032 1.005 1.038 1.049 1.024 1.019 1.074 1.045 1.052 1.058 1.023 1.049 1.045 1.035 1.043 1.023 1.032 1.035 1.018 1.043 1.011 0.999 1.017 0.994 0.998 1.000 0.995 1.024 0.989

PSO [18] 1.019 1.038 1.044 1.039 1.040 1.029 1.020 1.016 1.015 1.033 1.059 1.049 1.021 1.012 1.018 1.023 1.014 1.015 1.015 1.017 1.030 1.020 1.017 1.018 1.042 1.029 1.029 1.042 1.054 1.058 1.031 1.039 1.015 1.029 1.021 1.026 1.038 1.024 1.022 1.061 1.032 1.033 1.038 1.037 1.037 1.031 1.031 1.029 1.008 1.028 1.039 1.019 1.027 1.031 0.994 1.013 0.997 1.000 0.997 1.020 1.004 1.008

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PSO [18] 1.085 1.042 1.080 0.968 1.075 1.022 1.078 1.049 1.077 1.082 0.956 1.080 1.087 0.960 1.100 0.961 1.036 1.091 0.970 1.039 1.083 0.976 1.010 0.953 0.967 1.093 1.097 1.089 1.086 0.966 1.078 0.950 0.972 0.971 0.960 1.078 1.078 0.956 0.964 0.974 1.024 0.961 0.956 0.954 0.958 1.016 1.099 0.969 0.965 1.087 1.037 1.092 1.075 0.959 1.011 1.090 1.003 1.000 1.008 1.032 0.944 0.906

CLPSO [18] 1.033 1.055 0.975 0.966 0.981 1.009 0.978 1.079 1.080 1.028 1.030 0.987 1.015 0.961 0.985 1.015 1.084 0.983 1.051 0.975 0.983 0.963 0.971 1.025 1.000 1.077 1.048 0.968 0.964 0.957 0.976 1.024 0.965 1.073 1.030 1.027 0.985 0.983 1.088 0.989 0.990 1.028 0.976 1.088 0.961 0.961 1.012 1.068 0.976 1.041 0.979 0.976 0.972 1.033 1.004 1.060 1.000 1.000 0.992 1.007 1.061 0.930

DMEA 1.010 1.062 1.051 1.072 1.012 1.020 1.021 1.040 1.027 1.049 1.060 1.046 0.910 0.932 0.959 1.016 1.021 0.980 1.002 1.020 1.006 0.969 0.990 0.971 0.969 0.990 0.992 1.004 1.024 1.068 1.031 1.028 1.019 1.015 1.004 1.026 1.004 1.010 1.020 1.060 1.032 1.041 1.036 1.019 1.028 1.030 1.026 1.052 1.031 1.028 1.026 1.091 1.030 1.001 0.950 1.007 0.964 0.958 1.001 0.990 1.020 0.972

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Table 11. Simulation results of IEEE −118 system (Continued) Control variables 𝑇𝑎𝑝 127 𝑄𝐶 34 𝑄𝐶 44 𝑄𝐶 45 𝑄𝐶 46 𝑄𝐶 48 𝑄𝐶 74 𝑄𝐶 79 𝑄𝐶 82 𝑄𝐶 83 𝑄𝐶 105 𝑄𝐶 107 𝑄𝐶 110 PG(MW) QG(MVAR) Reduction in PLOSS(%) Total PLOSS (Mw) NR* - Not reported.

Base case 0.935 0.140 0.100 0.100 0.100 0.150 0.120 0.200 0.200 0.100 0.200 0.060 0.060 4374.8 795.6 0 132.8

MPSO [18] 1.010 0.049 0.026 0.196 0.117 0.056 0.120 0.139 0.180 0.166 0.189 0.128 0.014 4359.3 604.3 11.7 117.19

PSO [18] 1.009 0.048 0.026 0.197 0.118 0.056 0.120 0.140 0.180 0.166 0.190 0.129 0.014 4361.4 653.5 10.1 119.34

PSO [18] 0.967 0.093 0.093 0.086 0.089 0.118 0.046 0.105 0.164 0.096 0.089 0.050 0.055 NR* * NR* 0.6 131.99

CLPSO [18] 0.957 0.117 0.098 0.094 0.026 0.028 0.005 0. 148 0.194 0.069 0.090 0.049 0.022 NR* NR* 1.3 130.96

DMEA 1.000 0.029 0.018 0.189 0.126 0.046 0.134 0.127 0.176 0.159 0.172 0.114 0.026 4430.2 628.2 12.72 115.90

Table 12. Comparison of real power loss Parameter PLOSS (MW)

Method EGA [20] 646.2998

Method EEA [21] 650.6027

Method CSA [21] 635.8942

DMEA 610.1249

5.

CONCLUSION In this work Dynamic Membrane Evolutionary Algorithm (DMEA) successfully solved the optimal reactive power problem. Proposed methodology merges the fusion and division rules of P systems with active membranes and with adaptive differential evolution (ADE), particle swarm optimization (PSO) exploration stratagem. In this paper, composition of the dynamic membrane algorithm along with the fusion, division rules are utilized to solve the optimal reactive power problem. In this work, Gaussian probability distribution is initiated to engender the accelerating coefficients of PSO. Proposed Dynamic Membrane Evolutionary Algorithm (DMEA) has been tested in standard IEEE 14, 30, 57,118,300 bus test system and simulation results show the projected algorithm reduced the real power loss extensively.

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iPark: automated smart parking system Rahman Atiqur Information and Communication Engineering, Chongqing University of Posts and Telecommunications, P. R. China

Article Info

ABSTRACT

Article history:

Parking problems became ubiquitous and are growing at an alarming rate in every major city. It causes parking problems which cause a traffic jam, driver’s frustration, and pollution. One time we visit different public places for example shopping center, multiplex movies hall & lodging house during carnivals or holidays, it makes the added parking difficult. Checking out a parking lot results in 40% to 50% of traffic jams. Due to this, car parking, in turn, causes the traffic issue. There are some problems associated with car parking like the way to control the amount of the car within the parking zone, monitoring the movement of the car in/outside of the parking zone, check whether there's an area inside for more cars or not and therefore the safety to park. This paper proposes an answer for these problems using the concept of the web of Things. iPark is a fully automated system that senses the entry and exit of a car, displays the entire number of cars parked within the parking zone on screen, and the way many free spaces are available within the parking lot.

Received Jun 27, 2020 Revised Feb 4, 2021 Accepted Mar 11, 2021 Keywords: Communication technologies Image processing Internet of things (IoT) Raspberry Pi4 Sensing unit Smart city

This is an open access article under the CC BY-SA license.

Corresponding Author: Rahman Atiqur School of Information and Communication Engineering Chongqing University of Posts andTelecommunications Chongqing, 400065, P.R. China Email: bulbul.cse.cu@gmail.com

1.

INTRODUCTION Usually, a lot of difficulties attain during a manual car parking scheme similar to control, time consumption, and gasoline wastage. The prevailing parking system doesn’t provide an efficient thanks to predicting and spot vehicle occupancy in real-time. Whenever we've to park a car within the parking structure, we've to manually look for a parking slot. This tricky increases when the parking organization is full or multi-storied. This originates traffic controlling difficulties and avoidable time feeding in blast epochs.

Hence, the prevailing system doesn’t enable better real-time monitoring and management of obtainable spaces within the parking lot. All this causes inconvenience for the people. We face various problems associated with car parking like the way to control the amount of the car within the parking zone, monitoring the movement of the car in/outside of the parking zone, check whether there's an area inside for more cars or not and therefore the safety to park. [1] I’ve implemented a sensible system by using various technologies and advanced researches. The smart parking system is implemented in many environments with various features, which solves the issues faced within the day to day activities.

The most idea behind the Smart Car Parking System is to assist the user to seek out areas where parking is out there and therefore the number of slots free therein area. My recommended system reduces the time taken to see space for the vehicle. It also helps in reducing fuel consumption. [2] My recommended system uses ultrasonic sensors to sense the car. [3] There are three tired functionalities, rock bottom level comprising the sensing functionality, a middle tier handling data forwarding, and therefore the upper-tier handling data storage, processing, and client interfaces. My recommended system uses image processing Journal homepage: http://ijaas.iaescore.com

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using the ANPR technique to detect the license plate of the car. [4]-[6] I've also added the functionality to calculate the wages automatically. The utilization of iOS technology combined with the recent advances in wireless applications is that the key to unraveling emerging parking problems. [7] Road Map: In Section 2 We talk about the literature review. Section 3 presents the Smart Car Parking System’s implementation details and describes how the system Works. Section 4 are about the idea of dataset.Section 5 gives an overview of all resultset found in my systems and Section 6 concludes the paper.

2. a.

b.

c.

d.

LITURATURE REVIEW The succeeding is some papers that were referenced for the development “Automatic Multilevel Car Parking System” in Int. J. of Electrical and Microelectronics Research, ISSN 2348-6988 Vol. 3, No. 2, pp: (438-441), Mon.: April-June 2015 by Gupta A., Jaiswar A., Agarwal Ha., Shankar Ch. [1]. In this article, the authors have presented and labeled the idea of an “automatic car parking system”, which can inevitably sense the entrance and leaving of the cars, number of cars shown on the LCD. This automated car parking system decreases the time consumed to check the space for the cars. At this point, the authors have advised the use of sensors to sense the existence of the car.

“Smart Parking System with Image Processing Capability”, I.J. Intelligent Systems, App., 2012,3, 41-47 available online Ap 2012 in MECS by Reza, M.F. Ismail, A. A. Rokoni, M.A.R Sarkar [2, 5, 6, 7]. This article has presented the Smart Parking Systems which take the info about vacant parking spaces, process it, and then place the car at an assured spot. As well, the authors have announced an idea of an ophthalmic character recognition technique, i.e. “ANPR” for license plate recognition of vehicles.

“Android-based Smart Parking System” in Int. J. of Innovative Research in Computer Engg Vol. 3, May 2015 by Pallavi M., Radha De., Samiksha Na., Shubhangi M., Shraddha Sa. [3]. in this article, the authors have offered a plan for an “Android-based smart Parking System” that controls the sum of cars to be parked in the selected parking zone. This is completed by computerizing the Parking and unloading of the vehicle with the aid of an Android Application. An Android application will aid the operator to catch out the precise parking slot assigned to him in the parking zone. Information will be read locally.

Commands to the assigned parking slot will be displayed to the operator [3].

“ASPS using Internet of Things (IoT)” in Int. Journal of Scientific and Research Publications, Vol. 5, No. 12, Dec 2015 629 ISSN 2250-3153 by Mr. Basavaraju S. R [4]. In this publication, the author has presented an idea of the Internet of Things (IoT) which shows a vigorous role in attaching the adjacent environmental kits to the setup. The Author has recommended the use of groupings of IoT like detecting, processing as well as connectivity of data. Similarly, the author presented a plan for a Smart Parking System by creating the use of IoT viable h/w such as Arduino UNO microcontroller which consumes less power.

3. IMPLEMENTATION DETAILS 3.1. System outline The system structural design displays the diagram of the smart parking system. At the entrance point, when the car arrives into the parking lot, web camera takes the image of license plates and the image processing entity is used to transform it into text layout and it is used to assign a parking slot which is then kept into databank. [4] When the vehicle is parked in the assigned parking slot, then sensing unit perceives the existence of a vehicle in the parking slot. The Raspberry Pi unit then processes this raw data and hold it into a database through the internet via Ethernet Port. [4] Figure 1 graphycally shows all the things.

The iOS application offers the precise route of the assigned parking slot to the operator. The application then proceeds the assigned parking slot number as an input and shows the route that the operator needs to track to touch the parking slot. [3] The data is retrieved locally. Figure 2 graphically shows how the iOS application works.

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Figure 1. System model of recommended smart car parking system

Figure 2. iOS application

3.2. Sections The recommended system is alienated into following five sections: a.

Perceiving parts The Ultrasonic Sensors are cast-off to sense the existence of the vehicle. Ultrasonic sensors are vicinity sensors. These sensors sense the existence of the somatic object without coming in communication with that object, so the lifecycle of these sensors is greater [8]. In this recommended system, we use HCSR04 ultrasonic distance calculating sensor which is competent to sense an object at distance covered from 1.5cm to 50.5cm. Ultrasonic sensor entails transmitter, receiver, and regulator unit with a trigger, echo, and I/O pinches. The data restrained by the sensors is composed [9]. b.

Raspberry Pi device It is the general-purpose computer unit, which processes the data composed by sensors and brings up to date the database. [10] The resultant modifications are redirected in the database and shown on the front termination. The Raspberry Pi unit processes the data directed from the sensors then sends it to the database with Ethernet ports using the internet. The data directed by the sensors are analog data. [11] The Raspberry Pi unit transforms that raw analog data into a digital layout. The digital data is cast-off and a default variety for car parking is agreed upon. A predefined range is associated with the range restrained by the sensors.

Depending on this standing of a parking lot is determined. c.

Ethernet ports For linking the Raspberry Pi unit to the database, Raspberry Pi’s Ethernet port is used. The Raspberry Ethernet port connects the Raspberry Pi Unit to the internet in a few minutes. [12] An Ethernet port is attached to the Raspberry Pi board which assists connectivity to the internet over the Ethernet. The Ethernet port doings as a gateway for the arrangement which is useful to contact online repositories. I have iPark: automated smart parking system (Rahman Atiqur)

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used standard Ethernet libraries delivered by the Raspberry Pi unit to read and write the information. The Raspberry Pi unit is associated with the database via the internet. [13] d.

Image processing I have used a method known as “RFID reader” in my recommended scheme. [14] The RFID reader is a device that usages optical character recognition on images to read car registration plates. [15]-[17] with the help of an inbuilt RFID camera, the system will capture a picture of the number plate of the car and I have designed a code that transforms it into text format which is further kept in the database inevitably. The javaanpr.jar file is cast-off for image processing. This file comprises numerous inbuilt libraries that are used for matching and processing the image [18]-[21]. The RFID Image retraction technique comprises of following steps: − Number plate region detection − Plate fragmentation − Feature mining and standardization of characters − Recognition of characters e.

iOS application An iOS application is developed using Eclipse. The iOS application aids the operator to find out the precise parking slot assigned to him/her in the parking zone. Data is retrieved locally. Instructions to the assigned parking slot are displayed to the operator [22].

3.3. Algorithm There are seven basic algorithms that the software needs for recognizing a license plate: − Plate localization – This method is liable for finding and separating the plate on the image. − Plate positioning and sizing – This method pays for the skew of the plate and amends the dimensions to the obligatory dimension. − Normalization –This method modifies the brightness, contrast of the picture. − Character segmentation –This method is cast-off to find individual characters on the plates of the vehicle. − Optical character recognition. − Syntactical/Geometrical analysis – This method is cast-off check characters and positions against country-specific instructions. − The averaging of the recognized value over several fields/images is completed to yield a more dependable and assured outcome. Particularly in the case of any solo image may cover an echoed light flash, be partly buried, or other short-term outcomes.

3.4. Experimental setup The succeedings are the hardware and software requests for the recommended scheme: a. Hardware requests − Raspberry Pi 4 board − HC-SR04 Ultrasonic Parking Sensors − REES52 Finest USB AB Cable − RFID reader Camera b. Software requirements − Arduino IDE installed Raspberry Pi4 device − JDK- Eclipse − Databank- MySQL

4.

DATASET The values from the ultrasonic parking sensors are a chunk of the dataset. The concentrated range of the sensors is 50.5 cm. The blind mess for the sensors is 1.5 cm. [23] the databank has passed for the time at which the vehicle was parked, the parking slot no. and standing. The standing of a parking slot can be empty (0), booked (1), parked (2), the input for the RFID camera is an image of the number plate.

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RESULTS AND DISCUSSION The next are the snapshots for the Automated Smart Parking System as shown in Figure 3.

Figure 3. Raspberry Pi integrated arduino monitor display

The beyond screenshot displays serialized monitor display used in Arduino integrated raspberry pi4 tool. When a vehicle is parked in the assigned parking slot, the serialized monitor displays the supreme distance of the vehicle from ultrasonic parking sensors. The screenshot displays supreme distance that ultrasonic parking sensors can sense is 51 cm for parking slot p1, p2, p3, and p4. Figure 4, This Screenshot Demonstrates Parking Status for Parking Slot P1, P2, P3, and P4 Depending upon whether a vehicle is Parked or Not

Figure 4. Displays the parking status

Figure 5, This Screenshot Displays Distance of Cars from Sensors at what time vehicle is parked in Parking Slot number P3 and P4. Therefore, It Displays Parking Status=1 for Parking Slot P3 and P4.

Meanwhile, No vehicles are parked in Slot P1 and P2, Their Status Ruins Unaffected. [24]

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Figure 5. Parking status

Figure 6, displays the admin login screen from where the admin can access the whole system using iOS apps. The Below Screenshot Displays an Unoccupied Parking Lot in the iOS Application. From the figure, we see that parking lots P, P2, P3, and P4 are vacant for the first time. When a lot is reserved then the occupied lot screenshot is displayed in the Figure 7. [25]

Figure 6. Admin login page

Figure 7. Displays the empty parking lot Figure 8 this Screenshot Displays the Parking directions for Parking Slot 1. From this figure, we observed that when an operator selects a lot P1 then it is occupied.

Figure 8. Screenshot of occupied parking lot Int J Adv Appl Sci, Vol. 10, No. 2, June 2021: 107 – 114

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CONCLUSION Today, the tricky of parking is remarkable as there is no appropriate idea in place. The present vehicle parking system is inadequate. To settle this tricky, I have implemented a Smart Parking System (iPark) which allows the parking of cars and thus lessens the time in use to check the space to be cast-off by showing the spot where the space for parking is vacant. In this article, a competent car parking system is recommended which rigorously diminishes the parking difficulties. This article displays how the parking tricky in crowded spaces can be controlled with a well-thought strategy. It aids the users to catch out the accessibility of a parking slot in the parking zone, get the accessibility setting, and touch to the assigned parking slot within the parking zone. It aids to marks the supervision tranquil on the manager side. It also saves the time of the users necessary for examining a parking slot. Thus, the planned smart parking system is simple, cost-effective, and more effective as compared to present systems and offers enhanced client service.

ACKNOWLEDGEMENTS All praise and thanks are to ALLAH Almighty. After that, I would like to express my profound appreciation concerning my supervisor, Professor Dr. Yun Li for his endless supervision, promising assistance as well as motivating disputes. I am obliged to the School of Information and Communications Engineering for their livelihood.

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[2] M. O. Reza, M. F. Ismail, A. A Rokoni, M. A. R Sarkar, “Smart Parking System with Image Processing Facility” in International Journal Intelligent Systems and Applications, vol. 3, pp. 41-47, 2012. [Online]. Available: https://www.researchgate.net/profile/MSarkar/publication/224910014_Smart_Parking_System_with_Image_Processing_Facility/links/00b7d53c8f20b206 22000000/Smart-Parking-System-with-Image-Processing-Facility.pdf.

[3] Pallavi M, Radha De, Samiksha Na, Shubhangi Mu, Shraddha Sa, “Android based Smart Parking System,” in International Journal of Innovative Research in Computer and Communication Engineering, vol. 3, no. 5, pp.

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[4] Mr. Basavaraju S. R, “Automatic Smart parking System using Internet of Things (IoT),” in International Journal of Scientific and Research Publications, vol. 5, no. 12, pp. 629-632, 2015. [Online]. Available: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.735.8030&rep=rep1&type=pdf#page=638.

[5] Serkan Ozbay, Ergun Ercelebi, “Automatic Vehicle Identification by Plate Recognition,” in World Academy of Science and Technology, vol. 9, pp. 222-225, 2007. [Online]. Available: https://static.scaytrase.ru/cnr/article-cnreng.pdf.

[6] Priyamvadha Krishnakumar, “Automatic Number Plate Recognition (ANPR) through smart Phones using Image Processing Techniques,” in IOSR Journal of VLSI and Signal Processing (IOSR-JVSP), vol. 4, no. 4, pp. 19-23, 2014.

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[8] A. Khanna, R. Anand, “IoT based smart parking system,” 2016 International Conference on Internet of Things and Applications (IOTA), Pune, India, 2016, pp. 266-270.

[9] W. Alsafery, B. Alturki, S. Reiff-Marganiec, K. Jambi, “Smart Car Parking System Solution for the Internet of Things in Smart Cities,” 2018 1st International Conference on Computer Applications & Information Security (ICCAIS), Riyadh, Saudi Arabia, 2018, pp. 1-5.

[10] M. Fraifer, M. Fernström, “Smart car parking system prototype utilizing CCTV nodes: A proof of concept prototype of a novel approach towards IoT-concept based smart parking,” 2016 IEEE 3rd World Forum on Internet of Things (WF-IoT), Reston, VA, USA, 2016, pp. 649-654.

[11] Shruthi Mudaliar, Shreya Agali, Sujay Mudhol, Chaitanya K Jambotkar, “IoT based smart car parking system,” International Journal of Advanced Research in Science, Engineering and Technology, vol. 5, no. 1, pp. 270-271, 2019.

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[12] Natarajan P. B, Samit Kumar Ghosh, “Design and implementation of smart car parking system using lab view,” International Journal of Pure and Applied Mathematics, vol. 120, no. 6, pp. 329-338, 2018. [Online]. Available: https://acadpubl.eu/hub/2018-120-6/9/835.pdf.

[1]

iPark: automated smart parking system (Rahman Atiqur)

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[13] Bachhav, Jayakshei Dadaji, M. A. Mechkul, “Smart car parking system,” International Research Journal of Engineering and Technology, vol. 4, no. 6, pp.3036-3038, 2017. [Online]. Available: https://www.irjet.net/archives/V4/i6/IRJET-V4I6741.pdf.

[14] Nandyal Suvarna, Sabiya Sultana, Sadaf Anjum, “Smart car parking system using arduino uno,” International Journal of Computer Applications, vol. 169, no. 1, pp. 0975-8887, 2017. [Online]. Available: https://www.ijcaonline.org/archives/volume169/number1/nandyal-2017-ijca-914425.pdf.

[15] B. M. Mahendra, S. Sonoli, N. Bhat, Raju, T. Raghu, “IoT based sensor enabled smart car parking for advanced driver assistance system,” 2017 2nd IEEE International Conference on Recent Trends in Electronics, Information & Communication Technology (RTEICT), Bangalore, India, 2017, pp. 2188-2193.

[16] P. Sadhukhan, “An IoT-based E-parking system for smart cities,” 2017 International Conference on Advances in Computing, Communications and Informatics (ICACCI), Udupi, India, 2017, pp. 1062-1066.

[17] Gandhi B. K, Rao M. K, “A prototype for IoT based car parking management system for smart cities,” Indian Journal of Science and Technology, vol. 9, no. 17, pp. 1-6, 2016. [Online]. Available: https://sciresol.s3.us-east2.amazonaws.com/IJST/Articles/2016/Issue-17/Article43.pdf.

[18] D. Vakula, Y. K. Kolli, “Low cost smart parking system for smart cities,” 2017 International Conference on Intelligent Sustainable Systems (ICISS), Palladam, India, 2017, pp. 280-284.

[19] Atiqur Rahman, Yun Li, “Automated smart car parking system using raspberry Pi 4 and iOS application,” International Journal of Reconfigurable and Embedded Systems, vol. 9, no. 3, pp. 229-234, 2020. http://ijres.iaescore.com/index.php/IJRES/article/view/20295.

[20] Yanxu Zheng, S. Rajasegarar, C. Leckie, “Parking availability prediction for sensor-enabled car parks in smart cities,” 2015 IEEE Tenth International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), Singapore, 2015, pp. 1-6.

[21] A. Khanna, R. Anand, “IoT based smart parking system,” 2016 International Conference on Internet of Things and Applications (IOTA), Pune, India, 2016, pp. 266-270.

[22] A. Roy, J. Siddiquee, A. Datta, P. Poddar, G. Ganguly, A. Bhattacharjee, “Smart traffic & parking management using IoT,” 2016 IEEE 7th Annual Information Technology, Electronics and Mobile Communication Conference (IEMCON), Vancouver, BC, Canada, 2016, pp. 1-3.

[23] T. N. Pham, M. Tsai, D. B. Nguyen, C. Dow, D. Deng, “A Cloud-Based Smart-Parking System Based on Internetof-Things Technologies,” in IEEE Access, vol. 3, pp. 1581-1591, 2015.

[24] M. B. Ahmad, A. A. Abdullahi, A. S. Muhammad, Y. B. Saleh, U. B. Usman, “The Various Types of sensors used in the Security Alarm system,” International Journal of New Computer Architectures and their Applications, vol. 9, no.

2, pp, 50-59, 2019.

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Available: https://www.researchgate.net/publication/340479748_The_Various_Types_of_sensors_used_in_the_Security_Alar m_system.

[25] M. B. Ahmad, M. Cavas, “A review advancement of security alarm system using internet of things (IoT),” International Journal of New Computer Architectures and their Applications, vol. 9, no. 2, pp.38-49, 2019.

[Online].Available: https://www.researchgate.net/publication/337544365_A_REVIEW_ADVANCEMENT_OF_SECURITY_ALARM _SYSTEM_USING_INTERNET_OF_THINGS_IoT.

BIOGRAPHY OF AUTHOR Mr. Rahman Atiqur received his Bachelor of Science (B.Sc) and Master of Engineering (M.Engg.) degree from the Department of Computer Science and Engineering at the University of Chittagong, Chittagong, Bangladesh. In profession, he worked in the Department of Computer Science and Engineering, University of Chittagong, Bangladesh as an Assistant Professor since April 2016. Former he was a lecturer in the Department of Computer Science and Engineering, University of Chittagong, Bangladesh. He is now conducting his Ph.D. research works under the Chinese Government Scholarships (CGS) Program at Chongqing University of Posts and Telecommunications, Chongqing, China. His current research interest lies in the field of edge computing-based IoT systems.

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Confirmatory factor analysis: Model testing of financial ratio's with decision support systems approach T. Husain1, Maulana Ardhiansyah2, Dedin Fathudin3 1Departement 2,3Department

of Information Systems, STMIK Widuri, Indonesia of Informatics Engineering, Universitas Pamulang, Indonesia

Article Info

ABSTRACT

Article history:

The decision support systems approach can be developed into both computer-based and quantitative analysis tools. This research uses a model test with a confirmatory factor analysis (CFA) technique on matrix covariance against SEM methods to measure financial ratios. DSS analysis using numerical calculations aided by mathematical models through six phases. The first three phases of a structured approach to building multivariate models and the next three phases, namely estimation, interpretation, and validation, are developing from data input that has been selected using LISREL Version 8.72. The Financial Ratio's testing model with a CFA approach derived into a mathematical (quantitative) model can explain the complexity of the relationship between the goodness-of-fit models (GOF) with a different approach from prior research. The goodnessof-fit test results in this study produced scores on each of the financial ratio measurement models at an accuracy level of CR of 78.49, TATO of 1.26, DER of 41.41, ROA of minus 0.033, and PBV of 540.92. This means that PBV has the highest standardized loading factors to determine the measurement of Financial Ratio's. The CFA measurement based on SEM can be used to make appropriate decisions and combine a model comparison and redevelopment of the CFA technique and model testing with other software such as SPSS, PLS, AMOS, and others.

Received Jun 5, 2020 Revised Nov 25, 2020 Accepted Jan 23, 2021 Keywords: Confirmatory factor analysis DSS approach Goodness-of-fit (GOF) Mathematical models

This is an open access article under the CC BY-SA license.

Corresponding Author: T. Husain Departement of Information Systems STMIK Widuri Palmerah Barat Street No. 353, South Jakarta - 12210, Indonesia Email: thusain050686@gmail.com

1.

INTRODUCTION Decision support systems approach can be developed into approaches or methods, both computerbased systems or by developing methods or standards for quantitative analysis tools. This function can be used to solve problems in making semi and unstructured decisions. According to Sharda, Delen, and Turban [1], that these key DSS abilities and characteristics permit decision-makers to make better, further orderly decisions promptly. Modeling implies transfiguring the real-world hassle into a relevant prototype structure (model); Turban et al. argue that mathematical model is one of the approaches derived from scientific management processes to describe a real-world problem with prototypes and algebraic expressions so that modeling solutions can be solved using fast and efficient approaches [2]. The classical statistical approach has focused on predicting observations through quantitative analysis, in particular, mathematical modeling based on the relationship of factors. [3]. Factor analysis is a statistical approach with a dual variable inspection technique that determines the main components and manifests the interrelations among variables. According to Hair et Journal homepage: http://ijaas.iaescore.com

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al. that factor analysis have the main objective to discover a scheme designate the output carried in the quantity of the native variables inside a recent information assemblage of refine [4]. Furthermore, to carry out a confirmatory factor analysis, it can use raw data as input data in the form of covariant matrices or temporary correlation matrices to confirm the factor must first define latent constituents because these factors cannot be measured directly but through indicators or measurements that represent the construct [5].

Several recent studies [6]-[9] have suggested that this research is a multivariate model using the Pair-Copula approach that functions of two variables simultaneously using a hierarchical model construct, bivariate copulae, and copula models (R-vine). Conditioning using simple building blocks, then canonical vine copulas involving both observed and latent variables allows tail, asymmetric, and non-linear dependence. Using a goodness-of-fit index for the least-squares modeling to simulate and compare the index with the model fit in the structural equation model and also a new goodness-of-fit approach of simulation Rvine specifications. According to Henseler and Sarstedt, the results can validate how well a model explains data differences [10]. The model SEM with maximum likelihood estimation (MLE) approach according to with standard error (SE) operates a model specification test and information matrix with the likelihood ratio (LR) statistic from Alberto Maydeu-Olivares research, these finding that is optimizing the SE's calculated in concern a mean-and variance alter LR script statistic for the look ahead to information matrix [11]. The customer satisfaction model of leasing enterprise users to entail 50 respondents of the tempt a sample in conjunction with the purpose of Pilai, Lambda, F, and Wilk’s test with the assist of SPSS from Rizkiana and Hendikawati research, these findings that three-factor of discriminant analysis far side of the z-score proceeds of the attestation which appeared the precision score of the model which somewhat upper at 54 percent [12].

The use of covariance-based simulation models involves 95 percent confidence intervals with sample n = 100 use dependent variables in pairs in determining covariances, such as the Vale–Maurelli approach that focuses on identifying and improving skewness scores and univariate kurtosis with covariance structures from Grønneberg and Foldnes research, these findings that when covariance is weakly correlated, results based on the method other simulations will potentially give similar results [13]. Computational cognitive engineering model compares differences in models through criteria based on predictive performance and generative models to see feasibility and simulations with a cognitive scientific approach from Palminteri et al., research. The results of computational engineering models can assist in realizing the mechanisms that manage thoughts and behavior to the other side of the generation of algorithms in the reproduction of the impact of cognitive aspects viz. one's behavior [14]. Botes et al. argue that arranged decision support systems to get a meter of backdated energy efficiency modeling options objectively operated to assist in the process of consideration in the decision-making using the weighted-sum method. These findings of the financial comparison appeared that Section 12L tax incentive of the monetary worth of the ascendancy amount of 10 percent also 33 percent if no medium were on hand to obtain the last model [15].

Shkeer and Awang argue that the Marketing Information System set up with a factor analysis study involving 100 respondents through KMO and Bartlett's test and component matrices from each item and internal reliability to measure instruments in the decision-making process resulting ineffectiveness in measuring marketing decision support systems [16]. T. Husain and Maulana Ardhiansyah argue that the simulation model of Financial Ratio can explain the comparison of the integrated model testing with DSS a particular statistical approach, i.e., Pair-Sample T-Test [17].

In the present study, the mathematical modeling based on the relationship of factors through CFA technique and SEM methods uses to confirm whether the construct tested has a standardized loading factor (SLF) score that meets the requirements for decision-making. This study uses a different approach from prior studies, where factor analysis based on SEM has not been used in previous studies. This model is considered powerful, which can explain the model's assessment through the stages of the SLF and goodness-of-fit (GoF) test. The option of research subjects is driven by a few studies of the CFA technique test based on the decision support system approach in the research of social science categories in Indonesia. The previous research is still limited and dominated by research on the exact or mathematical science studies related to DSS. Therefore, the importance of this research is to provide ideas to specify and test the model in a new framework for future research for a researcher. However, the current study tries to another focus, where covariance values through the CFA technique serve as a guide in developing a model DSS. The research aims to adapt the framework for focusing on secondary data, i.e., the release of the Indonesian Stock Exchange (IDX) which companies that conduct Initial Public Offerings (IPO) as fifty-five new issuer's in 2019 by adding data from the previous year's, in 2018 [18], who have met the requirements for using the maximum likelihood estimation (MLE) technique in SEM.

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2.

RESEARCH METHOD This study uses an interdependent method that aims to reduce the original variables to be analyzed.

The information used is still owned and developed, and it is known as an abstract concept [19]. DSS analysis utilizing numeral calculations assisted with arithmetic calculation or other quantitative models that can be expanded with a covariance matrix analysis approach with modeling. The developed paradigm consists of six stages. The first three stages of the structured approach are to construct a multivariate model. The next three stages are to estimate, interpret, and validate the factor model. These are additional steps to assist in selecting substitute variables, computational factor scores, or creating summary scales, for application to other multivariate techniques [4]. Table 1 is showing the definition and measurement model, Figure 1 is showing the framework of CFA using quantitative model and DSS approach and Table 2 is showing Characteristic of fit indices.

Table 1. The definition and measurement model [20] Definition Liquidity Ratios is appeared a firm's liquidity in giving short-range obligations or indebtedness that is scheduled.

Activity Ratio's are used to measure one of the efficiencies which the firm using an asset to generate sales Debt Ratio's are used to measure one of the enlargement of risk and return through the use of fixed cost financing Profitability Ratio's are used to measure one of the effectiveness levels of management in yielding profits Market Share Ratio's which is used to enumerate the contemporary share price, to special accounting values

Measurement 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐴𝑠𝑠𝑒𝑡𝑠

CR =

𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠

TATO =

DER=

𝑁𝑒𝑡 𝑆𝑎𝑙𝑒𝑠 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡

𝑆ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟𝑠 ′ 𝐸𝑞𝑢𝑖𝑡𝑦

ROA= PER=

𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠

𝑀𝑃 𝑝𝑒𝑟 𝑆ℎ𝑎𝑟𝑒𝑠 𝑜𝑓 𝐶/𝑆 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑝𝑒𝑟 𝑆ℎ𝑎𝑟𝑒

Financial Ratio's modeling with matrix covariance approach is compute as: R =  + 1

(1)

TATO =  + 2

(2)

DER =  + 3

(3)

ROA =  + 4

(4)

PER =  + 5

(5)

Model estimation, interpretation, and validation are developing from data input that has been selected using LISREL Version 8.72. This research uses a maximum likelihood estimation (MLE) technique, which requires ranges from 50-200 data observations. This research's objective invite involves a mathematical simulation model using data mining and structural equation modeling (SEM).

Several guidelines were used to assess the suitability index based on the research model with separate sample sizes, model changes, and error rates in model specifications to identify the various suitability indices [4]. If the developed model has a reasonable error approximate to resolve whether the model can produce the measurement output further tested or return to the previous phase [21].

Confirmatory factor analysis: model testing of financial ratio's with decision support … (T. Husain)

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ISSN: 2252-8814 Exploratory Type of Factor Analysis (what is being grouped or – variables or cases?)

Data Summarization and Identifying Structures, Data Reduction Index Capital Market Directory (ICMD, IDX – 2018-2019)

Research Design

Selecting a Factor Model

what, how, and amount of sample sizes

component & common factors analysis

Model Specification and Interpreting

Validation of the Factor Model Analysis

1. Standardized Loadings Factors (Score) 2. Goodness-of Fit (Statistics)

Selection, Computation and Creating of Financial Ratio’s score and scales

Confirmatory Respesification

Structural Equation Modeling (SEM)

Figure 1. The framework of CFA using quantitative model and DSS approach [3], [4], [20]

Table 2. Characteristic of fit indices Number of Stat. (Observe variables - m) = 12 2 CFI / TLI RNI SRMR The RMSEA

Index Cut off values based on model characteristics Insignificant p-values predicted 0.97 or preferable May not diagnose misspecification well Biased upward, use more indices Worth < 0.08 by CFI = 0.97 or higher

3. RESULTS AND ANALYSIS 3.1. Data summarization, identifying structures and data reductions The purpose of summarizing data in defining several specific factors is to achieve the representation of many constructs. This summarization process explores the combination of structures that have been defined in the measurement of the interrelationships between factors that allow for the specification of a small number of dimensions (factors) that illustrate part of the genuine variable. Data reduction also depends on factor loading but for identifying factors for further analysis with other techniques or forming estimations of themselves (factor scores or addition scales), which then restore the genuine variables after the analysis phase. This study uses five financial ratio measurement factors consists of CR, TATO, DER, ROA, and PER (proxy) obtained from prospectus reports and financial statements of fifty-five IPO companies in 2019 and reduced by two company so that the observation data that meet the subset of representative variables in this phase is 53 x 2 years of observation.

3.2. Designing a factor analysis model Factor analysis is designed as a basis for calculating data input and classification, for the grouping of observational data, measurement properties, and variables, as well as using the sample size requirements needed to analyze decision-making. The sample calculation in the previous phase was 106 data observations that have fulfilled the requirements in the estimation technique based on maximum likelihood estimation (MLE). Furthermore, consideration of these components' selection was conceptualized into a model with a confirmatory factor analysis (CFA) technique. Figure 2 is showing path diagram: initial model.

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Figure 2. Path diagram: initial model

3.3. Model specification and interpreting Model specifications designed in the path diagram are converted into covariance matrix equation structures consisting of: λ = covariance matrix between loading indicators of a factor  = the construct of each factors  = measurement error of each factors The estimated models in this study were tested using the LISREL Version 8.72 software. The model specification starts with the item validity test (indicator) to confirm a factor load standard with the provisions that if the t-value > t-critical or standardized loading factors (SLF) value was more than 0.5, then the indicator is declared valid or vice versa. Next, an evaluation of factor criteria carried out with an estimated model based on three measurement criteria, consists of absolute, incremental, and parsimonious fit measures (overall model fit) or known as Goodness-of-Fit Statistics (GOF).

3.4. Validation / deployment model The evaluation stage is executed pass two sub-tests i.e. − Standardized Loading Factors CR = 0.27FR + 78,49 TATO = −0.055FR + 1,26 DER = 0.29FR + 41,41 ROA = 0.22FR − 0,033 PBV = −1.65FR + 540,92 Financial Ratio's gives a very impact on the accuracy of each measurement, including CR of 78.49, TATO of 1.26, DER of 41.41, ROA of only minus 0.03, and PBV of 540.92. This means that PBV has the highest standardized loading factors to determine the measurement of Financial Ratio's. Figure 3 is showing path diagram: measurement model.

Figure 3. Path diagram: measurement model Confirmatory factor analysis: model testing of financial ratio's with decision support … (T. Husain)

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− Goodness-of-Fit Statistics (GOF) Chi-Square Test produces a score of 1.10 with a p-value of 0.95405. The CFI / TLI test yields a score of -8.82, which means it shows poor-fit. A standardized RMR 0.026 with an RMSEA of 0.00 results in a close-fit index. GFI and AGFI values of 1.00 also produce a close-fit index.

3.5. Analysis The CFA technique is operated to prove the accuracy of the model development value in this research through summarization, design, specification, and validation stages on the DSS approach passed down inside statistical in SEM with financial ratio's objects. These illustrations explain that designing a path diagram for measurement properties and detecting errors in the use of measurements at an early stage.

Hereafter, it specifies the design for the next stages to convert into a covariance matrix to interpret a forwarding decision-making model. In this research, the CFA technique using or known as first-order confirmatory in SEM used to see which measurements meet the factor load requirements. If the value is more than 0.5, then the measurement is considered valid or vice versa. Furthermore, goodness-of-fit (GoF) was executed based on the three criteria above to assess whether the model proposed in this study could be continued at the deployment stage or not. If it does not meet the model suitability assessment criteria index, then a re-specification or modification indices step can be made through a recommendation from the output when using the LISREL Version 8.72 application with change the initial syntax by correlating a pair of values between error variances. This finding presents the value of RMSEA as a basis for decision making to validate the model, which requires a value of less than 0.08.

Several studies show findings with each approach to answer research problems, such as the PairCopula approach by a hierarchical model construct with assessment through observed and latent variables [6]-[8]. The same is the case with the usage of GoF to explain a model; however, it uses an approach to partial least squares path modeling and also Kendall's-T copula model (R-vine) [10], [9] while this research uses a CFA technique and also adopted by the MLE approach but in this study did not calculated with variance alter LR and a mean test statistic [11]. Moreover, according to determine the significance of the function discriminant and testing average difference between several groups, this is also the same at the specification stage for testing the quality of the proposed measurement instrument [12], while this research uses an SLF confirmatory technique.

Covariance models with ViTA (Vine to Anything) were developed based on a multivariate distribution known as the R-Vines concept with high-level control specifically for the need data with nonnormality multivariate through the skewness and kurtosis score [13], while this research uses a GoF score viewed based on clause greater than 0.5 (p-values; Chi-Square score). With computational cognitive modeling, expectant models' simulation is obligatory to counterfeit the models and support definite cognitive function claims. However, they overlooked their predictive performance [14], while this research uses a CFI / TLI test yield score that is -8,82 viewed based on clause greater than 0.97 so it's very different from that clause. A systematic DSS as evaluation ingredient modeling as a base for decision-making used to a weighted-sum method to pick a final model which uses the monetary worth of the Section 12L tax incentive factor with a score between 0.1 to 0.33 [15], while in this research uses an RMR score that is 0.026 viewed based on a clause that meets the requirements is less than same with 0.08. The construct of marketing DSS with exploratory factor analysis (EFA) and KMO and Bartlett's test with yield valid and reliable instrument which is similar to this research looking at Chi-Square score and p-values [16], while pair-sample T-test with a yield of normality and Levene's test is evaluation and assessment of the model with the DSS approach as a comparative study [17]. Based on the above analysis, the CFA measurement on an SEM basis is considered to answer or represent the accuracy of several results of previous studies. DSS abilities permit decisionmakers to make preferable, orderly decisions promptly if conjointed with CFA measurement for specification modeling.

4.

CONCLUSION The Financial Ratio testing model with a CFA approach attain into a mathematical (quantitative) model can describe the complexity of the link betwixt the goodness-of-fit model (GOF). The determination of the number of samples ranging from 50-200 is suitable using the maximum likelihood estimation (MLE) technique. Chi-Square Statistics (χ2) of 1.10 with a p-value greater than 0.5 and the RMSEA score that shows a model that meets the close-fit criteria is the basis or reference that the model does not need to be carried out re-specification or improvement. The goodness-of-fit test results in this study produced scores on each of the financial ratio measurement models at an accuracy level of CR of 78.49, TATO of 1.26, DER of 41.41, ROA of minus 0.033, and PBV of 540.92. This means that PBV has the highest standardized loading factors to determine the measurement of Financial Ratio's.

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The measurement of CFA based on SEM can be used as a consideration in making appropriate decisions. This research proposes practical resolves for hereafter investigation that integrate consolidate a model appeal and redevelopment of the CFA so that model testing can be useful for the denomination of how well another path model can describe distinct sets of data and use other software such as SPSS, PLS, AMOS, and others.

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Confirmatory factor analysis: model testing of financial ratio's with decision support … (T. Husain)

International Journal of Advances in Applied Sciences (IJAAS) Vol. 10, No. 2, June 2021, pp. 122~140 ISSN: 2252-8814, DOI: 10.11591/ijaas.v10.i2.pp122-140

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On optimization of manufacturing of a step-down DC-DC converter to increase integration density of elements E. L. Pankratov Department of Mathematical and Natural Sciences, Nizhny Novgorod State University, Nizhny Novgorod, Russia

Article Info

ABSTRACT

Article history:

We consider possibility to increase field-effect transistor's density in a switched-capacitor step-down DC-DC converter. Based on this approach we analyzed manufacturing of the converter in a heterostructure with special structure. Some specific sections of the heterostructure must be doped by ion implantation or by diffusion. After this procedure optimized annealing has been done. We also obtained conditions for decreasing of mismatch-induced stress value in this heterostructure. An analytical approach for analysis of heat and mass transport in multilayer structures has been introduced. The approach gives a possibility without crosslinking of solutions on interfaces between layers, take into account (i) spatial variation of parameters of considered processes; (ii) temporal variation of parameters of considered processes; (iii) nonlinearity of considered processes; (iv) mismatch-induced stress.

Received Jul 7, 2020 Revised Nov 10, 2020 Accepted Jan 23, 2021 Keywords: Increasing of element integration rate Optimization of manufacturing Switched-capacitor step-down DC-DC

This is an open access article under the CC BY-SA license.

Corresponding Author: E.L. Pankratov Mathematical and Natural Sciences Department Nizhny Novgorod State University 23 Gagarin avenue, Nizhny Novgorod, 603950, Russia Email: elp2004@mail.ru

1.

INTRODUCTION Currently density of elements of integrated circuits and their performance intensively increasing.

Simultaneously with increasing of the density of the elements of integrated circuit their dimensions decreases. One way to decrease dimensions of these elements of these integrated circuit is manufacturing of these elements in thin-film heterostructures [1]-[8]. An alternative approach to decrease dimensions of the elements of integrated circuits is using laser and microwave types annealing of dopant and/or radiation defects (these defects were generated during implantation of ions) [9]-[18]. Both types of annealing (laser and microwave) gives a possibility to obtain inhomogeneous distribution of temperature. Inhomogeneity of temperature leads to inhomogeneity of all temperature- dependent parameters (diffusion coefficient and other) due to the Arrhenius law. The inhomogeneity of properties of materials during doping gives a possibility to decrease dimensions of elements of integrated circuits [19]. Changing of properties of electronic materials could be obtain by using radiation processing of these materials [8], [9].

In this paper we consider a cascaded-inverter circuit based on field-effect transistors described in [4] see Figure 1. We assume, that the considered element has been manufactured in heterostructure from Figure 1. The heterostructure consist of a substrate and an epitaxial layer. The epitaxial layer includes into itself several sections manufactured by using another materials. The sections should be doped for generation into these sections required type of conductivity (n or p). We consider two types of doping: diffusion of dopant and implantation of ions of dopants. Framework this paper we analyzed redistribution of dopant

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during annealing of dopant and/ or radiation defects to formulate conditions for decreasing of dimensions of the considered a cascaded-inverter circuit.

Figure 1. The considered cascaded-inverter [4]

2.

METHOD OF SOLUTION

To solve our aim we shall analyze spatio-temporal distribution of concentration of dopant. The distribution has been determined by solving the following boundary problem [1], [3], [19]

 C x, y, z, t     C x, y, z, t     C x, y, z, t     C x, y, z, t    DC   DC   DC  t  x x y z   y   z 

(1)

Boundary and initial conditions could be written as (2).

 C  x, y , z , t   C x, y, z, t   C x, y, z, t   C  x, y , z , t  0 0, 0 0  x  y  y x x  Lx y 0 x 0 xL y

 C  x, y , z , t   C x, y, z, t   0 , C (x,y,z,0)=f (x,y,z) 0 z z x  Lz z 0

(2)

The function C(x,y,z,t) describes the distribution of dopant concentration in space and time; T is the annealing temperature; parameter DС describes the diffusion coefficient of dopant. Let us approximate considered dependences of diffusion coefficient of dopant on different parameters by using the relation, which has been obtained by analysis [20]-[22]  C   x, y , z , t    V  x, y , z , t  V 2  x, y , z , t   DC  DL  x, y , z , T  1      1   1 2  P  x, y , z , T    V* V * 2  

(3)

The dependence DL(x,y,z,T) is the independent on any concentrations part of dopant diffusion coefficient. The dependence P (x,y,z,T) is the dopant solubility limit. Value   [1], [3] is integer in the On optimization of manufacturing of a step-down DC-DC converter to increase … (E. L. Pankratov)

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considered interval [20]. Dependences V (x,y,z,t) is the radiation vacancies concentration distribution in space and time with equilibrium distribution V*. The considered dependence of diffusion coefficient of dopant on concentration C (x,y,z,t) has been discussed in [20]. It is known, that diffusion doping did not leads to generation of radiation defects and 1=2=0. We calculate distributions of radiation defects concentrations in space and time as solution of the equations, which are presented [21]-[23].  I x, y, z, t     I x, y, z, t     I x, y, z, t  2   DI x, y, z,T    DI x, y, z,T    kI , I x, y, z,T  I x, y, z, t   t x x  y  y    

   I x, y, z, t    DI x, y, z, T    kI ,V x, y, z, T  I x, y, z, t  V x, y, z, t  z  z 

(4)

 V x, y, z, t     V x, y, z, t     V x, y, z, t  2   DV x, y, z, T    DV x, y, z, T    kV ,V x, y, z, T V x, y, z, t   t x  x  y  y    

  V x, y, z, t    DV x, y, z, T    kI ,V x, y, z,T  I x, y, z, t  V x, y, z, t  z  z 

Initial conditions and boundary conditions could be written as (5).

   x, y , z , t     x, y , z , t     x, y , z , t   0 ,   x, y, z, t   0, 0, 0,  y x  x  y y 0 x  Lx x 0 yL y

  x, y, z, t   0 ,    x, y , z , t   0 ,  (x,y,z,0)=f (x,y,z) z z z 0 zL

(5)

z

Here are  =I,V. The considered function I (x,y,z,t) describes distribution of radiation interstitials concentration in space and time with equilibrium distribution I*; functions D(x,y,z,T) describe dependences of point radiation defects diffusion coefficients on spatial coordinates and temperature; terms V2(x,y,z,t) and I2(x,y,z,t) describe generation of divacancies and diinterstitials, respectively; function kI,V(x,y,z,T) describes dependences of recombination parameter of point radiation defects on spatial coordinates and temperature; functions kI,I(x,y,z,T) and kV,V(x,y,z,T) describe dependences of parameters of point radiation defects simplest complexes generation on spatial coordinates and temperature. Now let us calculate spatio-temporal distributions of divacancies V(x,y,z,t) and diinterstitials I(x,y,z,t) concentrations by solving of the equations, which are presented [21]-[23]

  I x, y, z, t      I x, y, z, t      I x, y, z, t    DI x, y, z, T    DI x, y, z, T   t x x y  y 

 V x, y, z, t     V x, y, z, t     V x, y, z, t    DV x, y, z, T    DV x, y, z, T   t x x y  y  

(6)

 V x, y, z, t    2 D x, y, z, T    kV ,V x, y, z, T V x, y, z, t   kV x, y, z, T V x, y, z, t   z  V z 

Initial conditions and boundary conditions could be written as (7).

   x, y, z, t  x

 0, x 0

   x, y, z, t  z

0, z 0

    x, y , z , t  x

    x, y , z , t  z

 0,

    x, y , z , t 

x  Lx

y

 0, y 0

   x, y, z, t  y

0, y  Ly

(7)

 0 , I (x,y,z,0)=fI (x,y,z), V (x,y,z,0)=fV (x,y,z). z  Lz

Functions D(x,y,z,T) describe dependences of diffusion coefficients of simplest complexes of point radiation defects on spatial coordinates and temperature; functions kI(x,y,z,T) and kV(x,y,z,T) describe Int J Adv Appl Sci, Vol. 10, No. 2, June 2021: 122 – 140

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dependences of parameters of decay of the considered complexes on spatial coordinates and temperature. We obtain spatio-temporal distributions of point radiation defects concentrations concentrations framework approach, which has been recently elaborated [19]. Framework the approach we transform diffusion coefficients approximations to the next form: D(x,y,z,T)=D0[1+ g(x,y,z,T)]. Here D0 describe the diffusion coefficients average values, 0<1, |g(x,y,z,T)|1,  =I,V. The same transformation we used for approximations of generation of their complexes parameters and recombination of point defects: kI,V(x,y,z, T)=k0I,V[1+I,V gI,V(x,y,z,T)], kI,I(x,y,z,T)=k0I,I[1+I,I gI,I(x,y,z,T)] and kV,V(x,y,z,T)=k0V,V [1+V,V gV,V(x,y,z,T)].

Here k01,2 are the averaged values of the considered parameters, 0I,V<1, 0I,I<1, 0V,V<1, | gI,V(x,y,z, T)|1, | gI,I(x,y,z,T)|1, |gV,V(x,y,z,T)|1. Let us introduce the following dimensionless variables:  = x/Lx,

~ ~   D0 I D0V t L2 , I x, y, z, t   I x, y, z, t  I * , V x, y, z, t   V x, y, z, t  V * ,   L2 k 0 I ,V

,  = y /Ly,    L k0  , 2

D0 I D0V

D0 I D0V ,  = z/Lz. After using of these variables we obtain (4) and conditions (5) in the

following form ~  I  , , ,   



D0 I



 

D0 I D0 I D0V

D0 I

~ ~   I  , , ,      I  , , ,           1   g  ,  ,  , T  1   g  ,  ,  , T     I I I I       

~    I  , , ,   ~ (8)     1   g  ,  ,  , T     1   I ,V g I ,V  , , , T  I  , , ,   I I    

D0 I D0V D0 I D0V ~ ~  V  , , ,    I 1   I , I g I , I  , , , T  I 2  , , , 

   , , ,     , , ,     , , ,   ~  , , ,   0,  0, 0  0,        1  0  1  0 ~

~

~

f   , ,  ,   ~  , ,  ,   ~  , ,  ,  ~  0,  0 ,   , ,  ,   *    0  1

(9)

We calculate solutions of (8) with account conditions (9) by using approach, which was introduced recently [18]. Framework the approach we determine the required solution as

~  , ,  ,      i   j   k ~ijk  , ,  ,   





i 0

j 0

k 0

(10)

After substitution of the above series (10) into recently considered (8) with conditions (9) leads to obtaining

of equations for the zero-order approximations of point radiation defects concentrations I 000  , , ,  and

~

~ ~ ~ V000  , ,  ,  . Also we obtain corrections for them I ijk  , , ,  and Vijk  , , ,  , i 1, j 1, k 1 based

on the substitution. We present the obtained equations in Appendix in the end of the paper. We solved the obtained equations by Fourier approach in the standard form [24], [25]. We present the obtained solutions in the Appendix in the end of the paper. Now let us calculate of point radiation defects of simplest complexes distributions of concentrations in space and time. Let us transform diffusion coefficient's approximations to the next form: D(x,y,z,T) =D0[1+g(x,y,z,T)]. Here D0 are the averaged means of the considered diffusion coefficients. After this transformation we obtain (6) in this form

  I x, y, z, t      I x, y, z, t  2  D0I 1   I gI x, y, z,T    kI , I x, y, z,T  I x, y, z, t   kI x, y, z,T   t x x   I x, y, z, t   D0I

    I x, y, z, t      I x, y, z, t  1   I gI x, y, z,T    D0I 1   I gI x, y, z, T    y y  z z  

 V x, y, z, t     V x, y, z, t  2  D0V 1   V gV x, y, z,T    kI , I x, y, z,T  I x, y, z, t   kI x, y, z,T   t x x   I x, y, z, t   D0V

   V x, y, z, t     V x, y, z, t  1   V gV x, y, z, T    D0V 1   V gV x, y, z, T    y y  z z   

On optimization of manufacturing of a step-down DC-DC converter to increase … (E. L. Pankratov)

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After considered transformation we will determined solution of obtained equations in the following form (11).

  x, y, z, t     i    i x, y, z, t  

i 0

(11)

Substitution of the considered series into above equations and conditions for them leads to obtaining equations for functions Ii(x,y,z,t) and Vi(x,y,z,t) (for i 0) and conditions for them. We present the obtained equations and conditions in the Appendix in the end of this paper. We solved the obtained equations by Fourier approach in the standard form [24], [25]. We present the obtained solutions in the Appendix in the end of the paper.

Now let us determine spatio-temporal distribution of dopant concentration by using the same approach, which we used for solution of equations of radiation defects. In this situation we again transform approximation of diffusion coefficient (now diffusion coefficient of dopant) to the same form as for diffusion coefficient of radiation defects: DL(x,y,z,T)=D0L[1+ LgL(x,y,z,T)]. Here D0L is the averages mean of diffusion coefficient of dopant, 0L<1, |gL(x,y,z,T)|1. Now let us to solve.(1) as the following form:

C x, y, z , t     Li   j Cij x, y, z , t  



i 0

j 1

Now we take into account this series into (1) and relations (2). After this accounting we obtain equations for all functions Cij(x,y,z,t) (for i 0, j 0) and conditions for them. The obtained equations and conditions for them are presented in the Appendix. We solved the obtained equations by Fourier approach in the standard form [24], [25] and present these solutions in the Appendix in the end of paper.

In this paper we analyzed spatio-temporal distributions of radiation defects and infused or implanted dopant concentrations. To make the analysis we used the second-order approximations of these concentrations on all parameters, which were used framework obtained solutions. Usually the considered approximation is enough good approximation to obtain some quantitative results and make some qualitative analysis. All obtained analytical results were checked by comparison with results of numerical simulation.

3.

DISCUSSION

Now we make analysis of spatio-temporal distributions of dopant with account redistribution of radiation defects. We present on Figure 2 typical distributions of dopant concentration in space near interface between layers of heterostructures. We obtain the considered distributions for the following case: diffusion coefficient of dopant in doped area is larger, than the same coefficient in the nearest undoped areas. Under the condition the Figure 2 shows increasing of compactness of dopant distributions framework the fieldeffect heterotransistors (increasing of number of curves on these figures describes larger difference between magnitudes of coefficients of diffusion of dopant in layers of the considered heterostructure). At the same time one can find, that homogeneity of distribution of dopant concentration increases. Vice versa relation between values of diffusion coefficients of dopant leads to vice versa result see Figure 3, increasing of number of curves on these figures describes larger difference between magnitudes of coefficients of diffusion of dopant in layers of the considered heterostructure). It is necessary to note, that using the considered approach of manufacturing of field-effect heterotransistors leads to necessity optimization of value of annealing time of the considered dopant. We optimize the annealing time by using the criterion, which has been recently introduced [26]-[32]. To make the optimization we approximate real distribution of concentration of dopant by step-wise function  (x,y,z). These approximations are presented on Figure 4. The considered value of optimal annealing time we obtained by minimization of mean-squared error

U

1 Lx L y Lz    C x, y, z ,     x, y, z  d z d y d x Lx Ly Lz 0 0 0

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(12)

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127

2.0 1

C(x,y,z,)

1.5

2 3

4

1.0 Epitaxial layer

Substrate

0.5

0.0

L /4

0

L /2 x

(a)

L

3 L /4

(b)

Figure 2. These figures are; (a) Distributions of infused dopant concentration, (b) Distributions of implanted dopant concentration. Curve 1 and curve 3 describe distribution of dopant at time of annealing  = 0.0048(Lx2+Ly2+Lz2)/D0. Curve 2 and curve 4 describe distribution of dopant at time of annealing  = 0.0057(Lx2+Ly2+Lz2)/D0 1.2

fC ( x )

1.00000

1 2

0.10000

1 Substrate

0.8

C(x,)

C(x,)

0.01000

0.4

2

0.00100 0.00010 0.00001 0.00000

0.0

- a 1 =- L /3

0

x

L /2 x x

L /4

0

L

a =2 L /3

(a)

0

L

3 L /4

(b)

Figure 3. These figures are; (a) Distributions of infused dopant concentration, (b) Distributions of implanted dopant concentration. Solid lines describe distributions dopant in heterostructure, which includes into itself two layers: substrate and epitaxial layer. Dushed lines describe distributions dopant in a single layer

2

1

C(x,)

2

C(x,)

3 4

3 1

4

Lx

0

(a)

0

x

Lx

(b)

Figure 4. These figures are; (a) Infused dopant distributions. Curve 1 describes idealized step-wise distribution. Curve 2, curve 3 and curve 4 describe actually existing distributions of concentration of dopant at different means of time of annealing, (b) Implanted dopant distributions. Curve 1 describes idealized stepwise distribution. Curve 2, curve 3 and curve 4 describe actually existing distributions of concentration of dopant at different means of time of annealing On optimization of manufacturing of a step-down DC-DC converter to increase … (E. L. Pankratov)

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Dependences of optimal means of time of annealing on different parameters were presented on Figure 5. Standard procedure after ion implantation is annealing of generation during the implantation radiation defects. During ideal annealing of defects dopant should achieves nearest interface between layers of considered heterostructure. If the considered dopant do not achieved the interface the annealing, than it is attracted an interests additional annealing of dopant. In this situation annealing time from Figure 5b is smaller, than analogous time from Figure 5a.

0.5

0.12

2

2

0.4

4 -2

4

 D0 L

 D0 L

-2

0.08

0.3 3

0.2

3

0.04

1

1

0.1 0.00

0.0 0.0

0.1

0.2 0.3 a/L , , , 

0.4

0.5

(a)

0.0

0.1

0.2 0.3 a/L , , , 

0.4

0.5

(b)

Figure 5. These figures are; (a) Dimensionless optimized time of annealing of infused dopant as a function of several parameters. Curve 1 as a function of dimensionless optimized time of annealing on relation a/L and  =  = 0 at the equal values to each other of dopant diffusion coefficient in all materials of heterostructure.

Curve 2 as a function of dimensionless optimized time of annealing of the parameter  at a/L=1/2 and  =  = 0. Curve 3 as a function of dimensionless optimized time of annealing on parameter  at a/L=1/2 and  =  = 0.

Curve 4 as a function of dimensionless optimized time of annealing of parameter  at a/L=1/2 and  =  = 0. (b) Dimensionless optimal annealing time of implanted dopant as a function of several parameters. Curve 1 describes the dependence of the annealing time on the relation a/L and  =  = 0 for equal to each other values of dopant diffusion coefficient in all parts of heterostructure. Curve 2 describes the dependence of the annealing time on value of parameter  for a/L=1/2 and  =  = 0. Curve 3 describes the dependence of the annealing time on value of parameter  for a/L=1/2 and  =  = 0. Curve 4 describes the dependence of the annealing time on value of parameter  for a/L=1/2 and  =  = 0

In this section, it is explained the results of research and at the same time is given the comprehensive discussion. Results can be presented in figures, graphs, tables and others that make the reader understand easily [2], [5]. The discussion can be made in several sub-chapters.

4.

CONCLUSION

Based on modelling of redistribution of implanted and infused dopants in heterostructures during formation of field-effect heterotransistors in switched-capacitor step-down DC-DC converter we formulate recommendations to modify technological process for decreasing of dimensions of the considered transistors and with simultaneous increasing of their de Nsity. We also formulate several recommendations for decreasing of mismatch-induced stress in heterostructures. As an accompany result of this paper we introduce an analytical approach for prognosis of mass and heat transport during manufacturing of elements of integrated circuits.

APPENDIX

Functions I ijk  , , ,  and Vijk  , ,  ,  described by the following equations for any values

~

~

of indexes i 0, j 0, k 0

Int J Adv Appl Sci, Vol. 10, No. 2, June 2021: 122 – 140

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ISSN: 2252-8814

~  I 000  , ,  ,   

~ ~ ~ D0 I   2 I 000  , ,  ,   2 I 000  , ,  ,   2 I 000  , ,  ,       D0V   2  2  2 

~  V000  , ,  ,   

~ ~ ~ D0V   2V000  , ,  ,   2V000  , ,  ,   2V000  , ,  ,      ; D0 I   2  2  2 

~  I i 00  ,   





D0 I D0V

129

~ ~ ~ D0 I   2 I i 00  , , ,   2 I i 00  , , ,   2 I i 00  , , ,       D0V   2  2  2 

~ ~   I i 100  , , ,     I i 100  , , ,         g  ,  ,  , T  g  ,  ,  , T   I   I               

~  I i 100  , , ,         g  ,  ,  , T  I   , i 1,     

~ ~ ~ ~ ~ Vi 00  ,  D   2V  , , ,   2Vi 00  , , ,   2Vi 00  , , ,  D0V   Vi 100  , , ,     0V  i 00 2    g  ,  ,  , T    V  D0 I    2  2 D0 I      



~ D0V    Vi100  , , ,     g  ,  ,  , T  V  D0 I    

~  I 010  , , ,   

~ D0V    Vi100  , , ,     g  ,  ,  , T  V  , i 1, D0 I     

~ ~ ~ D0 I   2 I 010  , , ,   2 I 010  , , ,   2 I 010  , , ,       D0V  2  2  2 

~ ~  1   I ,V g I ,V  , ,  , T  I 000  , ,  ,  V000  , ,  , 

~  V010  , ,  ,   

~ ~ ~ D0V   2V010  , ,  ,   2V010  , ,  ,   2V010  , ,  ,       D0 I   2  2  2 

~ ~  1   I ,V g I ,V  , ,  , T  I 000  , ,  , V000  , ,  , 

~  I 020  , ,  ,   

D0 I D0V

~ ~ ~   2 I 020  , ,  ,   2 I 020  , ,  ,   2 I 020  , ,  ,        2  2  2  





~ ~ ~ ~  1   I ,V g I ,V  , ,  , T  I 010  , ,  ,  V000  , ,  ,   I 000  , ,  , V010  , ,  , 

~  V020  , ,  ,   

~ ~ ~ D0 I   2V020  , ,  ,   2V020  , ,  ,   2V020  , ,  ,       D0V   2  2  2 





~ ~ ~ ~  1   I ,V g I ,V  , , , T  I 010  , , , V000  , , ,   I 000  , , , V010  , , , 

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ISSN: 2252-8814

~  I 001  , , ,   

~ ~ ~ D0 I   2 I 001  , , ,   2 I 001  , , ,   2 I 001  , , ,       D0V  2  2  2 

~2  , , ,   1   I , I g I , I  , , , T  I 000

~ V001  , , ,   

~ ~ ~ D0V   2V001  , , ,   2V001  , , ,   2V001  , , ,       D0 I  2  2  2 

~2  , ,  ,   1   I , I g I , I  , ,  , T  V000

~ ~ ~ ~  I110  , , ,  D0 I   2 I110  , , ,   2 I110  , , ,   2 I110  , , ,  D0 I       g I  , , ,T     2 2 2  D0V     D0V    

~ ~ ~  I 010  , , ,     I 010  , , ,     I 010  , , ,       g I  , , ,T    g I  , , ,T              





~ ~ ~ ~  1   I , I g I , I  , , , T  I100  , , , V000  , , ,   I 000  , , , V100  , , , 

~ ~ ~ ~ V110  , , ,  D0V   2V110  , , ,   2V110  , , ,   2V110  , , ,   D0V       gV  , , ,T     2 2 2  D0 I     D0 I    

~ ~ ~ V010  , , ,    V010  , , ,    V010  , , ,       gV  , , ,T    gV  , , ,T              





~ ~ ~ ~  1  V ,V gV ,V  , , , T  V100  , , ,  I 000  , , ,   V000  , , ,  I100  , , , 

~  I 002  , ,  ,   

D0 I D0V

~ ~ ~   2 I 002  , ,  ,   2 I 002  , ,  ,   2 I 002  , ,  ,        2  2  2  

~ ~  1   I , I g I , I  , ,  , T I 001  , ,  ,  I 000  , ,  , 

~  V002  , ,  ,   

~ ~ ~ D0V   2V002  , ,  ,   2V002  , ,  ,   2V002  , ,  ,       D0 I   2  2  2 

~ ~  1   V ,V gV ,V  , ,  , Е V001  , ,  ,  V000  , ,  ,  

~  I101  , ,  ,   



D0 I D0V

      

~ ~ ~ D0 I   2 I101  , ,  ,   2 I101  , ,  ,   2 I101  , ,  ,       D0V   2  2  2 

~ ~   I 001  , ,  ,     I 001  , ,  ,      g  ,  ,  , T  g  ,  ,  , T  I   I        

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Int J Adv Appl Sci

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ISSN: 2252-8814

131

~  I 001  , ,  ,     ~ ~   g  ,  ,  , T  I    1   I g I  , ,  , T  I100  , ,  , V000  , ,  ,      



~  V101  , ,  ,   

D0V  D0 I

D0V D0 I

~ ~ ~   2V101  , ,  ,   2V101  , ,  ,   2V101  , ,  ,       2 2 2        

~ ~   V001  , ,  ,     V001  , ,  ,       gV  , ,  , T    gV  , ,  , T            

~  V001  , ,  ,     ~ ~    g  ,  ,  , T  V    1   V gV  , ,  , T  I 000  , ,  , V100  , ,  ,      



~ ~ ~ ~  I 011  , , ,  D0 I   2 I 011  , , ,   2 I 011  , , ,   2 I 011  , , ,   ~ ~       I 010  , , ,  I 000  , , ,   2 2 2  D0V     

~ ~  1   I , I g I , I  , , , T   1   I ,V g I ,V  , , , T  I 001  , , ,  V000  , , ,  ~ ~ ~ ~  V011  , , ,  D0V   2 V011  , , ,   2 V011  , , ,   2 V011  , , ,   ~ ~       V010  , , ,  V000  , , ,   2 2 2  D0 I     

~ ~  1   V ,V gV ,V  , , , T  1   I ,V g I ,V  , , , t  I 000  , , ,  V001  , , ,  Conditions for considered functions are

 ~ijk  , ,  ,  

0,

 ~ijk  , , ,  

x 0

 ~ijk  , ,  ,  

0,

0, x 1

 ~ijk  , ,  ,  

 0

 ~ijk  , , ,  

0,  0

 ~ijk  , , ,  

0,  1

 0 (i 0, j 0, k 0);  1

~ 000  , ,  ,0  f   , ,    ,  ijk  , ,  ,0   0 (i 1, j 1, k 1)

~

*

Solutions of the considered equations are

~000  , , ,   Here Fn 

F0  L



2   Fn c   c   c   en    L n 1





1 1 1 1 cos  n u   cos  n v  cos  n w f n u, v, w d w d v d u , enI    exp   2 n 2 D0V D0 I , cn() *   0 0 0





= cos ( n ), enV    exp   2 n 2 D0 I D0V ;

~  1 1 1 I D0 I  ~ i 100 u, v, w,                I i 00  , ,  ,   2 n c  c  c  e  e   s u c v   n  nI  n  n  nI n  1 D0V u 0 0 0 0  cn w g I u, v, w, T  d w d v d u d   2

 1 1 D0 I   n cn  c  c enI    enI     cn u   sn v   D0V n 1 0 0 0

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132

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  cn w g I u, v, w, T  1

0

~   I i 100 u, v, w,  D0 I  d w d v d u d   2  n cn  c  c  enI    enI     v D0V n1 0

~  I i 100 u , v, w,    cn u  cn v  sn w g I u , v, w, T  d w d v d u d  , i 1, w 0 0 0 1

1

1

 1 1 1 D0V  ~ Vi 00  , ,  ,   2  n cn  c  c enV    enI     sn u  cn v  gV u, v, w, T   D0 I n1 0 0 0 0

~  1 1 Vi 100 u,  D0V   cn w d wd v d u d   n cn  c  c enV    enI     cn u  sn v   u D0 I n1 0 0 0 

1

1

1

0

0

0

0

  enI     cn u  cn v  sn w gV u , v, w, T 

~ Vi 100 u ,  d w d v d u d  , i 1. w

Here sn() is sin ( n );

~010  , , ,   2  cn  cn  cn  en    en     cn u   cn v  cn w 1   I ,V g I ,V u , v, w, T   



1

1

1

n 1

0

0

0

0

~ ~  I 000 u, v, w,  V000 u, v, w,  d w d v d u d   1 1 1 D0 I   cn  cn   cn  en    en    cn u  cn v  cn w 1   I ,V g I ,V u, v, w,T   D0V n 1 0 0 0 0

~020  , , ,   2





~ ~ ~ ~  I 010 u, v, w, V000 u, v, w,   I 000 u, v, w, V010 u, v, w,  d w d v d u d  



1

1

1

n 1

0

0

0

0

~001  , ,  ,   2  cn   cn   cn   en    en     cn  u   cn  v  cn  w 





2 u, v, w, d w d v d u d   1    ,  g  ,  u, v, w,T  ~000





1

1

1

n 1

0

0

0

0

~002  , ,  ,   2  cn   cn   cn   en    en     cn u   cn v   cn w 





 1    ,  g  ,  u, v, w, T  ~001 u, v, w,  ~000 u, v, w, d w d v d u d  ~ I110  , ,  ,   2  g I u, v, w, T 

 1 1 1 D0 I   n cn  cn  cn  enI    enI     sn u   cn v   cn u   D0V n1 0 0 0 0

~  I i 100 u, v, w,  d w d v d u d   2 u

Int J Adv Appl Sci, Vol. 10, No. 2, June 2021: 122 – 140

D0 I   n cn  cn  cn  enI    D0V n1

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~  I i 100 u, v, w,  D0 I   enI     cn u   sn v  cn u  g I u, v, w, T  d w d v d u d   2  v D0V 0 0 0 0 

1

1

1





1

1

1

n 1

0

0

0

0

  n enI    enI    cn u  cn v   sn u  g I u , v, w, T 

~  I i 100 u, v, w,  d wd v d u d  w

 cn  cn  cn    2  cn  enI  cn  cn   enI     cn u   cn v   cn v 1   I ,V g I ,V u , v, w, T   



1

1

1

n 1

0

0

0

0





~ ~ ~ ~  g I ,V u , v, w, T  I100 u , v, w, V000 u , v, w,   I 000 u , v, w, V100 u , v, w,  d w d v d u d   1 1 1 D0V   n cn  cn  cn  enV    enV     sn u   cn v   cn u   D0 I n1 0 0 0 0

~ V110  , ,  ,   2

~  Vi 100 u, v, w,  D0V   gV u, v, w, T  d w d v d u d   2  n cn  cn  cn  enV    u D0 I n1

~  Vi 100 u, v, w,    enV     cn u   sn v  cn u  gV u, v, w, T  d w d v d u d   2 v 0 0 0 0 

1

1

1





1

1

1

n 1

0

0

0

0

  n enV    enV    cn u  cn v   sn u  gV u , v, w, T 

D0V  D0 I

~  Vi 100 u , v, w,  d wd v d u d  w

 cn  cn  cn    2  cn  enI  cn  cn   enV     cn u   cn v   1   I ,V g I ,V u, v, w, T   



1

1

1

n 1

0

0

0

0





~ ~ ~ ~  cn w I100 u, v, w, V000 u, v, w,   I 000 u, v, w,  V100 u, v, w,  d w d v d u d   1 1 1 D0 I  ~ I101  , ,  ,   2  n cn  cn  cn  enI    enI     sn u   cn v  g I u, v, w, T   D0V n1 0 0 0 0

 I u, v, w,   cn w 001 d w d v d u d   2 ~

u

  sn v  cn wg I u, v, w, T  1

1

0

0

D0 I   n cn   cn   cn   enI    D0V n1

~  I 001 u, v, w,  D0 I  d w d v d u d   2  n enI  cn  cn  cn    v D0V n1

~   I 001 u, v, w,    enI     cn u  cn v   sn w g I u, v, w, T  d w d v d u d   2  cn  cn  cn    n 1 w 0 0 0 0 

1

1

1

 1 1 1 ~ ~  enI    enI    cn  u   cn  v   cn  w 1   I ,V g I ,V u, v, w, T I100 u, v, w,  V000 u, v, w,  d w d v d u d  0

0

0

0

 1 1 1 D0V  ~ V101  , , ,   2  n cn  cn  cn  enV    enV     sn u   cn v  gV u, v, w, T   D0 I n 1 0 0 0 0

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~  1  V001 u, v, w,  D0V   cn w d w d v d u d   2  n cn   cn   cn   enI   enV     cn u   u D0 I n 1 0 0   sn v  cn wg I u, v, w, T  1

1

0

0

~  I 001 u, v, w,  D0 I  d w d v d u d   2  n enI  cn  cn  cn    v D0V n 1

~   V001 u , v, w,    enV     cn u  cn v   sn w gV u , v, w, T  d w d v d u d   2  cn  cn  cn    n 1 w 0 0 0 0 

1

1

1

 1 1 1 ~ ~  enV    enV    cn  u   cn  v   cn  w 1   I ,V g I ,V u, v, w, T I100 u, v, w,  V000 u, v, w,  d w d v d u d  0

0

0

0



 1 1 1  ~ ~ I 011  , ,  ,   2  cn   cn   cn   enI    enI     cn  u   cn  v   cn  w I 000 u , v, w,   n 1

0

0

0

0



~ ~ ~  1   I , I g I , I u, v, w, T I 010 u, v, w,   1   I ,V g I ,V u, v, w, T I 001 u, v, w, V000 u, v, w,  d w d v d u d 



 1 1 1  ~ ~ V011  , ,  ,    2  cn   cn   cn   enV    enV     cn  u   cn  v   cn  w I 000 u , v, w,   n 1

0

0

0

0



~ ~ ~  1   I , I g I , I u, v, w, T I 010 u, v, w,   1   I ,V g I ,V u, v, w, T I 001 u, v, w, V000 u, v, w,  d w d v d u d  Equations for the considered functions i(x,y,z,t), i 0 could be written as

  2  I 0 x, y, z, t   2  I 0 x, y, z, t   2  I 0 x, y, z, t    I 0 x, y, z, t   D0I     t  x2  y2  z2    k I , I x, y, z, T  I 2 x, y, z, t   k I x, y, z, T  I x, y, z, t 

  2 V 0 x, y, z, t   2 V 0 x, y, z, t   2 V 0 x, y, z, t   V 0 x, y, z, t   D0V     t  x2  y2  z2    kV ,V x, y, z, T V 2 x, y, z, t   kV x, y, z, T V x, y, z, t    2  I i  x, y , z , t   2  I i  x, y , z , t   2  I i  x, y , z , t     I i  x, y , z , t    D0 I      D0 I   g I x, y, z , T   2 2 2 t x y z  x  



  I i 1 x, y, z , t       I i 1 x, y, z , t       I i 1 x, y, z , t      g I  x , y , z , T    g I  x , y , z , T    , i 1, y y z  y   z  

  2V i x, y, z , t   2V i x, y, z , t   2V i x, y, z , t    V i x, y, z , t    D0 V      D0 V   g V x, y, z , T   2 2 2 t x y z  x  

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135

 V i 1 x, y, z , t      V i 1 x, y, z, t      V i 1 x, y, z , t      g V  x , y , z , T    g V  x , y , z , T    , i 1, y y z  y   z  



Initial and boundary conditions for the considered functions could be written as

   i x, y, z, t  x

 0,

   i  x, y , z , t  x

x 0

   i x, y, z, t  z

0,

0, x  Lx

   i  x, y , z , t  z

z 0

   i  x, y , z , t  y

 0, y 0

   i x, y, z, t  y

0, y  Ly

 0 , i 0; 0(x,y,z,0)=f (x,y,z), i(x,y,z,0)=0, i 1., z  Lz

Solutions of the considered equations are

  0 x, y, z, t  

F0  Lx Ly Lz

2  2   Fn  cn x cn  y cn z en  t    n cn x cn  y  cn z  e  n t   Lx Ly Lz n 1 L n 1



t

Lx

Ly

Lz

0

0

0

0





  e  n     cn u   cn v   cn w kI , I u, v, w,T  I 2 u, v, w,   kI u, v, w,T  I u, v, w,  d w d v d u d Lx

Ly

Lz

0

0

0







Here Fn    cn u   cn v   cn w f   u, v, w d w d v d u , en  t   exp   2 n2 D0 t Lx2  Ly2  Lz2 ;

  i  x, y , z , t   

 cn w

Ly Lx Lz t 2              n c x c y c z e t e   s u   n  n  cn v   g   u, v, w, T   n n n n 2 Lx Ly Lz n 1 0 0 0 0

  I  i 1 u, v, w,  u

t

Lx

Ly

Lz

0

0

0

0

d w d v d u d 

t 2          n c x c y c z e t e  n       n n n  n Lx L2y Lz n1 0

  e  n     cn u   sn v   cn w g  u, v, w,T 

t

Lx

Ly

Lz

0

0

0

0

 cn z  e  n t  e  n     cn u   cn v   sn w

  I  i 1 u, v, w,  v

d w d v d u d 

  I  i 1 u , v, w,  w

2   n cn x  cn  y   Lx Ly L2z n 1

g   u , v, w, T  d w d v d u d , i 1.

Functions Cij(x,y,z,t) describes by the following equations for any values of indexes i 0, j 0

 C00 x, y, z, t   2C00 x, y, z, t   2C00 x, y, z, t   2C00 x, y, z, t   D0 L  D  D 0L 0L t  x2  y2  z2

  2Ci 0 x, y, z, t   2Ci 0 x, y, z, t   2Ci 0 x, y, z, t   Ci 0 x, y, z, t   g L x, y, z,T    D0 L      D0 L 2 2 2 t x y z x    C01 x, y, z, t   2C01 x, y, z, t   2C01 x, y, z, t   2C01 x, y, z, t   D0 L  D  D  0L 0L t  x2  y2  z2

On optimization of manufacturing of a step-down DC-DC converter to increase … (E. L. Pankratov)

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 D0 L

  C00 x, y, z, t   C00 x, y, z, t    C00 x, y, z, t   C00 x, y, z, t      D0 L    x  P x, y, z, T  x  y  P x, y, z, T  y  

 D0 L

  C00 x, y, z, t   C00 x, y, z, t     z  P x, y, z, T  z 

 C02 x, y, z, t   2 C02 x, y, z, t   2 C02 x, y, z, t   2 C02 x, y, z, t   D0 L  D  D  0 L 0 L t  x2  y2  z2    C  1 x, y, z , t   C00 x, y, z , t     C00 1 x, y, z , t   C00 x, y, z , t      D0 L   C01 x, y, z , t  00  C x , y , z , t   01  P  x, y , z , T  x P   x, y , z , T  y   x   y 



    C00 1 x, y, z , t   C00 x, y, z , t        C00  x, y, z , t   C00 x, y, z , t     C x , y , z , t  D 0L   01     z  P   x, y , z , T  z x       x  P  x, y , z , T 



  C00 x, y, z , t   C01 x, y, z , t     C00 x, y, z , t   C01 x, y, z , t             y  P   x, y , z , T  y  z P x , y , z , T  z    

 C11 x, y, z, t   2C11 x, y, z, t   2C11 x, y, z, t   2C11 x, y, z, t   D0 L  D  D  0 L 0 L t  x2  y2  z2  C  1 x, y, z , t   C00 x, y, z , t     C00 1 x, y, z , t   C00 x, y, z , t        D0 L  C10 x, y, z , t  00  C x , y , z , t   10  P  x, y , z , T  x P   x, y , z , T  y   y   x 



    C00 1 x, y, z , t   C00 x, y, z , t        C00 x, y, z , t   C10 x, y, z , t     C x , y , z , t  D 0L   10     z  P   x, y , z , T  z x       x  P  x, y , z , T 



     C00 x, y, z , t   C10 x, y, z , t     C00 x, y, z, t   C10 x, y, z, t     C01 x, y, z, t           D0 L   g L x, y, z ,T    y  P  x, y , z , T  y z x   x    z  P  x, y , z , T    



 C01 x, y, z , t      C01  x, y, z , t       g L  x, y , z , T    g L  x, y , z , T   y y z  z  

Initial and boundary conditions for the considered functions takes the form

 Cij x, y, z, t   C ij x, y, z, t  0, x x x 0

0, x  Lx

 C ij  x, y, z , t   Cij  x, y, z , t   0, y  y y 0

0, y  Ly

 Cij x, y , z , t   Cij x, y, z, t   0 , i 0, j 0; C00(x,y,z,0)=fC (x,y,z), Cij(x,y,z,0)=0, i 1, j 1. 0, z z z  Lz z 0 Solutions for the above equations are

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 F0C 2   FnC cn x  cn  y  cn z  enC t  Lx Ly Lz Lx Ly Lz n 1



Ly Lx Lz  1 1 1   , FnC   cn u   cn v   f C u, v, w cn w d w d v d u ;    L2 L2 L2  0 0 0 y z   x

Here enC t   exp   2 n 2 D0C t 



Ci 0  x, y , z , t   

 cn w

Ly Lx Lz t 2   n FnC cn x cn  y cn z enC t  enC     sn u   cn v   g L u , v, w, T   L Ly Lz n 1 0 0 0 0 2 x

t  Ci 10 u, v, w,  2  d wd v d u d   n FnC cn x  cn  y  cn z  enC t  enC     2 u Lx Ly Lz n 1 0

Lx

Ly

Lz

0

0

0

  cn u   sn v   cn v  g L u , v, w, T 

 Ci 10 u , v, w,  2  d wd v d u d   n FnC enC t   v Lx Ly L2z n 1

t

Lx

Ly

Lz

0

0

0

0

 cn x cn  y cn z   enC     cn u   cn v   sn v  g L u, v, w, T  C01 x, y, z , t   



 Ci 10 u, v, w,  d wd v d u d w

Ly Lx Lz t 2              n F c x c y c z e t e   s u   nC  n  cn v   cn w nC n n n nC 2 Lx Ly Lz n 1 0 0 0 0

C00 u , v, w,   C00 u , v, w,  2  d wd v d u d   n FnC cn  x  cn  y  cn  z  enC t    P u , v, w, T  u Lx L2y Lz n 1 t

Lx

Ly

Lz

0

0

0

0

  enC     cn u   sn v   cn w

C00 u, v, w,   C00 u, v, w,  2  d wd v d u d   n enC t    P u, v, w, T  v Lx Ly L2z n 1

t

Lx

Ly

Lz

0

0

0

0

 FnC cn x cn  y cn z   enC     cn u   cn v   sn w C02 x, y, z , t     C01 u , v, w, 

C00 u, v, w,   C00 u, v, w,  d wd v d u d P  u, v, w, T  w

Ly Lx Lz t 2              n F c x c y c z e t e   s u   nC  n  cn v   cn w  nC n n n nC 2 Lx Ly Lz n 1 0 0 0 0

C00 1 u , v, w,   C00 u , v, w,  2  d wd v d u d   FnC cn x  cn  y   P u , v, w, T  u Lx L2y Lz n 1

t

Lx

Ly

Lz

0

0

0

0

 n cn z  enC t   enC     cn u   sn v   C01 u, v, w,   cn w d w d v d u d     sn wC01 u , v, w,  Lz 0

C00 1 u, v, w,   C00 u, v, w,   P u, v, w, T  v

Ly Lx t 2              n F c x c y c z e t e   c u     cn v   nC n n n nC nC n Lx Ly L2z n 1 0 0 0

C00 1 u , v, w,   C00 u , v, w,  2  d wd v d u d  2  n cn  x    P u , v, w, T  w Lx Ly Lz n 1

On optimization of manufacturing of a step-down DC-DC converter to increase … (E. L. Pankratov)

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138

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Lx

Ly

Lz

0

0

0

0

 FnC cn  y  cn z  enC t   enC     sn u   cn v   cn wC01 u, v, w, 



 C00 u, v, w,   u

Lx t C00 1 u , v, w,  2  d wd v d u d   n FnC cn x  cn  y  cn z  enC t   enC     cn u    2 P u , v, w, T  Lx Ly Lz n 1 0 0

Ly

Lz

0

0

  sn v   cn w C01 u, v, w, 

C00 1 u , v, w,   C00 u , v, w,  2  d wd v d u d   n  P u, v, w, T  v Lx Ly L2z n 1

t

Lx

Ly

Lz

0

0

0

0

 FnC cn x cn  y cn z enC t  enC     cn u   cn v   sn wC01 u, v, w, 



C00 1 u, v, w,   P u, v, w, T 

Ly Lx t  C00 u , v, w,  2  d wd v d u d  2  n FnC cn x cn  y cn z  enC t   enC     sn u   cn v   w Lx Ly Lz n 1 0 0 0

Ly

Lz

0

0

  cn v   cn w

C00 u , v, w,   C01 u , v, w,  2  d wd v d u d   n FnC cn x  cn  y  cn z  enC t    P u , v, w, T  u Lx L2y Lz n 1

t

Lx

Ly

Lz

0

0

0

0

  enC     cn u   sn v   cn w

C00 u , v, w,   C01 u , v, w,  2  d wd v d u d   n FnC cn x  cn  y    P u , v, w, T  v Lx Ly L2z n 1

t

Lx

Ly

Lz

0

0

0

0

 cn z enC t   enC     cn u   cn v   sn w C11 x, y, z, t   

Ly Lx Lz t 2   C01 u , v, w,                n F c x c y c z e t e   s u c v       cn w nC n n n nC nC n n 2 Lx Ly Lz n 1 u 0 0 0 0

 g L u , v, w, T  d w d v d u d    g L u , v, w, T  Lz 0

Lz

0

0

Ly Lx Lz t 2                n F c x c y c z e t e   c u s v      cn w  nC n n n nC nC n n Lx L2y Lz n 1 0 0 0 0

Ly Lx t  C01 u , v, w,  2              d wd v d u d  n F c x c y c z e t e   c u   nC  n  cn v   nC n n n nC v Lx Ly L2z n 1 0 0 0

  sn w g L u, v, w,T  Ly

C00 u, v, w,   C01 u, v, w,  d wd v d u d P u, v, w,T  w

 n  cn v   cn w

Lx t  C01 u, v, w,  2  d wd v d u d  2  n FnC cn x cn  y cn z enC t  enC     sn u   w Lx Ly Lz n 1 0 0

t C00 u , v, w,   C10 u , v, w,  2  d wd v d u d   n cn x  cn  y  cn z enC t   enC      2 P u, v, w, T  u Lx Ly Lz n 1 0

Lx

Ly

Lz

0

0

0

 FnC  cn u   sn v   cn w

C00 u, v, w,   C10 u, v, w,  2  d wd v d u d   FnC cn x cn  y cn z enC t    P u, v, w, T  v Lx Ly L2z n 1

t

Lx

Ly

Lz

0

0

0

0

 n  enC     cn u   cn v   sn w

C00 u, v, w,   C10 u , v, w,  2  d wd v d u d  2  FnC cn x cn  y cn z    P u, v, w, T  w Lx Ly Lz n 1

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Int J Adv Appl Sci

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t

Lx

Ly

Lz

0

0

0

0

 n enC t  enC     sn u   cn v   cn wC10 u , v, w, 



139

C00 1 u , v, w,   C00 u , v, w,  2 d wd v d u d   P u, v, w, T  u Lx L2y Lz



t

Lx

Ly

Lz

n 1

0

0

0

0

  n FnC cn x cn  y cn z enC t  enC     cn u   sn v   C10 u, v, w,   cn wd w d v d u d  



C00 1 u, v, w,   C00 u, v, w,   P u, v, w,T  v

Ly Lx Lz t 2  n FnC cn x cn  y cn  z enC t  enC     cn u   cn v   sn wC10 u , v, w,   2  Lx Ly Lz n 1 0 0 0 0

C00 1 u, v, w,   C00 u, v, w,  d wd v d u d P u, v, w, T  w

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International Journal of Advances in Applied Sciences (IJAAS) Vol. 10, No. 2, June 2021, pp. 141∼148 ISSN: 2252-8814, DOI: 10.11591/ijaas.v10.i2.pp141-148

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A numerical algorithm to find a root of non-linear equations using householder’s method Srinivasarao Thota Department of Applied Mathematics, School of Applied Natural Sciences, Adama Science and Technology University, Adama, Ethiopia

Article Info

ABSTRACT

Article history:

In this paper, we propose a three step algorithm using Householder’s method for finding an approximate root of the given non-linear equations in one variable. Several numerical examples are presented to illustrate and validation of the proposed method.

Implementation of the proposed algorithm in Maple is also discussed with sample computations.

Received Nov 24, 2020 Revised Feb 2, 2021 Accepted Apr 15, 2021 Keywords:

This is an open access article under the CC BY-SA license.

Non-linear equations Iterative method Householder’s method Approximate root Maple implementation Corresponding Author: Srinivasarao Thota Department of Applied Mathematics School of Applied Natural Sciences Adama Science and Technology University Post Box No. 1888, Adama, Ethiopia Email: srinithota@ymail.com, srinivasarao.thota@astu.edu.et

1.

INTRODUCTION Finding an approximate solution of a given non-linear equation is one of the important topics in numerical analysis. Many mathematical models of physics, economics, engineering, science and any other disciplines come up with non-linear equations of the type . In resent time, several scientists and engineers have been focused on to solve the non-linear equations both numerically and analytically. In the literature, there are several iterative methods/algorithms available using different techniques such as homotopy, interpolation, Taylor’s series, quadrature formulas, decomposition etc. with modifications and improvements, and different hybrid iterative methods, see, for example [1]-[17]. There are several methods available to find an approximate solution of non-linear systems also, see for example, [18]-[23]. In generally, the roots of non-linear or transcendental equations cannot be expressed in closed form or cannot be computed analytically. The root-finding algorithms provide us to compute approximations to the roots; these approximations are expressed either as small isolating intervals or as isolating point numbers. In this paper, we use the Householder’s technique to create a three-step iterative algorithm for solving the given non-linear equation of single variable with converging order more than or equal to four. Indeed, we focus on creating a tree-step algorithm to find a root of a given non-linear equation using the well-known techniques namely, Householder’s technique and modified Newton’s method. We also focus on its Maple implementation with sample computations. The proposed algorithm is simple to understand and efficient than some existing methods.

Since, we focus on creating an efficient and simple three-step algorithm using Householder’s method and modified Newton’s method, we recall basic concepts related to the existing methods. In this paper, we Journal homepage: http://ijaas.iaescore.com

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consider the non-linear equations of the following type (1). f (x) = 0,

(1)

where f : I → R is a scalar function in single variable for an open interval I ⊆ R and continuously differentiable function. In numerical analysis, the order of convergence of a convergent sequence are quantities that represent how quickly the sequence approaches its limit. The order of converges of any iterative method is defined [13] as |en+1 | ≤ c|en |p , where p is the order of convergence and c is a positive finite constant. Householder’s method is one of the famous methods in producing a sequence of approximation roots of (1) with initial point x0 . The Householder’s method has cubic order of convergence [1]-[2] and is given as (2) xn+1 = xn −

(f (xn ))2 f 00 (xn ) f (xn ) , n = 0, 1, 2, . . . . − f 0 (xn ) 2(f 0 (xn ))3

(2)

In the literature, there are several modifications of Householder’s method have been developed and analyzed by various techniques, for example, see [1]-[3], [24]. The modified Householder’s methods give better performance than the Newton’s method.

Recall the predictor-corrector method developed by Traub [4] in 1864 as follows, for f 0 (xn ) 6= 0, f (xn ) , f 0 (xn ) f (yn ) xn = yn − 0 . f (yn ) yn = xn −

(3)

A modified Newton’s method developed by McDougall and Wotherspoon [25] is converged faster than √ the Newton’s method with a convergence order 1 + 2, and it is given as follows: Let x0 = y0 , for n = 0 (initially), compute f (x0 ) , x1 = x0 − 0 f (x0 ) and for n ≥ 1, yn = xn − xn+1 = xn −

f (xn ) f0

xn−1 +yn−1 2

f (xn ) f0

xn +yn 2

, (4)

.

If xn = yn , for all n in equation (4), then the modified Newton’s method developed by McDougall and Wotherspoon becomes Newton’s predictor-corrector method as given in equation (3). The rest of paper is organized as follows: Section 2. presents the methodology and steps involving in the proposed algorithm and the flow chart; Section 3. presents couple of numerical examples to illustrate and validate the proposed algorithm; and Section 4. presents the Maple implementation of the proposed algorithm with sample computations.

2.

PROPOSED ITERATIVE ALGORITHM In this section, we present a three-step iterative algorithm using the well-known Householder’s method given in (2) and a modified newton’s method given in equation (4). The proposed iterative formula under consideration is given as: set x0 = y0 , for n = 0 (initially), compute x1 = x0 −

(f (x0 ))2 f 00 (x0 ) f (x0 ) − , f 0 (x0 ) 2(f 0 (x0 ))3

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and for n ≥ 1, yn = xn −

xn+1 = xn −

f (xn ) f0

xn−1 +yn−1 2

−

(f (xn ))2 f 00 (xn )

3 , n−1 2 f 0 xn−1 +y 2

(f (xn ))2 f 00 (xn )

3 . xn +yn − n 2 f 0 xn +y 2 2

(5)

f (xn ) f0

If xn = yn , for all n and f 00 (xn ) 6= 0 in equation (4), then the proposed algorithm becomes Householder’s predictor-corrector method and it has fourth-order convergence [3, 24]. If xn = yn for all n and f 00 (xn ) = 0 in (4), then the proposed algorithm becomes Newton’s predictor-corrector method as given in (3).

2.1. Steps for calculating root The following steps are involved to compute an approximate root of a given using the proposed algorithm.

1. Choose an initial approximation x0 ∈ R with x0 = y0 for n = 0.

2. Compute x1 using formula given in (5). i.e., x1 = x0 −

(f (x0 ))2 f 00 (x0 ) f (x0 ) − , 0 f (x0 ) 2(f 0 (x0 ))3

3. For n ≥ 1, compute yn and xn+1 using the proposed algorithm. i.e., yn = xn −

xn+1 = xn −

f (xn ) f0

xn−1 +yn−1 2

f (xn ) f0

xn +yn 2

−

−

(f (xn ))2 f 00 (xn )

3 , n−1 2 f 0 xn−1 +y 2

(f (xn ))2 f 00 (xn ) 3 . n 2 f 0 xn +y 2

4. Repeat Step 3 until we get desired approximate root, for n = 1, 2, 3 . . ..

Flow chat of the proposed algorithm is presented in Figure 1.

Figure 1. Flow chat of the proposed algorithm A numerical algorithm to find a root of non-linear equations...(Srinivasarao Thota)

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3.

NUMERICAL EXAMPLES In this section, we present couple of numerical examples to illustrate the proposed algorithm and comparisons are made to confirm that the algorithm gives solution faster than existing methods.

Consider the following nonlinear equation to compute an approximate root using the proposed method. f (x) = xex − 1.

(6)

The exact root of the equation is x = 0.5671432904. Suppose the initial approximation is x0 = 3. The stopping condition is corrected to ten decimal places. Set x0 = y0 = 3, compute x1 as follows x1 = x0 −

f (x0 ) (f (x0 ))2 f 00 (x0 ) = 1.922456285. − f 0 (x0 ) 2(f 0 (x0 ))3

Now, we compute yn and xn+1 , for n = 1, using the proposed algorithm, as follows y1 = x1 − x2 = x1 −

f (x1 ) f0

x0 +y0 2

f (x1 ) f0

x1 +y1 2

−

(f (x1 ))2 f 00 (x1 ) 3 = 1.767472904, 0 2 f 0 x0 +y 2

−

(f (x1 ))2 f 00 (x1 ) 3 = 0.9087794052.

1 2 f 0 x1 +y 2

Similarly, we can compute yn and xn+1 , for n > 1, using the proposed algorithm, as follows y2 = 0.8380960197, x3 = 0.5661945014, y3 = 0.5667781506, x4 = 0.5671428368, y4 = 0.5671432908, x5 = 0.5671432903, y5 = 0.5671432904, x6 = 0.5671432904.

Hence the required approximate root of the given (6) is 0.5671432904 up to ten decimal places and with the tolerance error 1 × 10−10 . The graphical representations (using Maple) of the iterations values at different iterations is shown in Figure 2, absolute errors at different iterations are shown in Figure 3 and absolute function values at different iterations are shown in Figure 4.

Figure 2. Iterations at different iterations

Figure 3. Absolute errors at different iterations

Figure 4. Absolute function values at different iterations

The following non-linear equations with initial approximations to compare the number of iterations taken to obtain the approximate root using existing methods and proposed method. For simplicity, we take Int J Adv Appl Sci, Vol. 10, No. 2, June 2021 : 141 – 148

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tolerance error 1 × 10−8 . f1 (x) = x2 − (1 − x)5 , 3

f2 (x) = x − e

−x

x0 = 5.0,

,

x0 = 6.0,

x 1 f3 (x) = −20x5 − + , 2 2 f4 (x) = cos(x) − x3 , x

x0 = 1.5, x0 = 8.0,

3

f5 (x) = (e + x − 20) ,

x0 = 4.0,

f6 (x) = x − 3 ln(x),

x0 = 0.5.

We compare the proposed method with various existing methods such as Newton’s Method (NM), Kang et al.

Method (KM) [26], McDougall-Wotherspoon Method (MWM) [25], Neamvonk Method (ANM) [27]-[29] and Proposed Method (PM) to show the efficiency of the proposed method. Table 1, shows the number of iterations taken by various methods to obtain the required approximate root.

Table 1. Comparison of iterations by different methods for example 3 Function f1 (x) f2 (x) f3 (x) f4 (x) f5 (x) f6 (x)

Approx. Root 0.345954815848 0.772882959149 0.427677296931 0.865474033102 0.865474033102 0.865474033102

NM 12 10 10 10 44 7

KM 6 5 5 5 14 4

MWM 9 7 8 7 33 5

ANM 6 6 6 6 10 5

PM 6 4 4 4 12 2

From Table 1, one can observe that the proposed method (PM) gives the required approximate root faster than the other existing methods (i.e., in lowest iteration number).

4.

MAPLE IMPLEMENTATION OF PROPOSED ALGORITHM In this section, we present the implementation of the proposed algorithm in Maple.

Input: given f (x), initial approximation x[0], tolerance , correct to decimal places δ, maximum number of iterations n.

Output: approximate solution.

4.1. Pseudo-code − Set x[0] = y[0] and compute x[1] using formula in (5). − for i from 1 to n do − compute y[i] and x[i+1] using formulas in (5). − if abs(x[i + 1] − x[i]) < and abs(f (x[i + 1])) < δ then break; − output x[i + 1] 4.2. Maple programming We present the maple code of the proposed algorithm as follows. > > > > >

eps := TYPE; # epsilon value epsabs := TYPE; # delta value f(x):= TYPE; # given non-linear equation fd:=D(f); fdd:=D(D(f)); A numerical algorithm to find a root of non-linear equations...(Srinivasarao Thota)

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> x[0] := TYPE; # initial approximation > y[0]:=x[0]; > n:= TYPE; # required number of iterations > x[1] := x[0]-(f(x[0]))/(fd(x[0]))((f(x[0]))∧ (2)*fdd(x[0]))/ (2*(fd(x[0]))∧ (3)): > for i from 1 to n do > y[i]:=x[i]-(f(x[i]))/(fd((x[i-1]+y[i-1])/(2)))(f(x[i]))∧ (2)fdd(x[i]))/(2*(fd((x[i-1]+y[i-1])/(2)))∧ (3)): > x[i+1] := x[i]-(f(x[i]))/(fd((x[i]+y[i])/(2)))((f(x[i]))∧ (2)*fdd(x[i]))/(2*(fd((x[i]+y[i])/(2)))∧ (3)): > abserror[i]:=abs(x[i+1]-x[i]); > absfun[i]:=abs(f(x[i+1])); > if abs(x[i+1]-x[i]) < eps or abs(f(x[i+1])) < epsabs > then break; > end if: > printf("Iteration No: %g = %10.10f\\n", i,x[i+1]); > end do; 4.3. Sample computations Recall the function f6 (x) from Example 3. to compute an approximate solution using the maple implementation. > eps := 0.00000001; > epsabs := 0.00000001; > f(x):= x-3 ln(x); > fd:=D(f); > fdd:=D(D(f)); > x[0] := 0.5;y[0]:=0.5; > n:= 15; > x[1] := x[0]-(f(x[0]))/(fd(x[0]))((f(x[0]))∧ (2)*fdd(x[0]))/ (2*(fd(x[0]))∧ (3)): > for i from 1 to n do > y[i]:=x[i]-(f(x[i]))/(fd((x[i-1]+y[i-1])/(2)))((f(x[i]))∧ (2)fdd(x[i]))/(2*(fd((x[i-1]+y[i-1])/(2)))∧ (3)): > x[i+1] := x[i]-(f(x[i])) / (fd((x[i]+y[i])/(2))) -((f(x[i]))∧ (2)*fdd(x[i])) /(2*(fd((x[i]+y[i])/(2)))∧ (3)): > abserror[i]:=abs(x[i+1]-x[i]); > absfun[i]:=abs(f(x[i+1])); > if abs(x[i+1]-x[i]) < eps or abs(f(x[i+1])) < epsabs then > break; > end if: > printf("Iteration No: %g = %10.10f\\n", i,x[i+1]); > end do; 1.10−8 1.10−8 x → x − 3 ln(x) 3 x→1− x 3 x→ 2 x 0.5 0.5 15 Int J Adv Appl Sci, Vol. 10, No. 2, June 2021 : 141 – 148

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1.430307717 1.850449158 0.515191954 0.004163965 Iteration No:1 = 1.8504491580 1.854014254 1.857200752 0.006751594 0.000010394 Iteration No:2 = 1.857183861 1.857183978 1.857183861 0.000016891 1.10−9

5.

CONCLUSION In this paper, we proposed a three-step iterative algorithm for finding an approximate root of a given non-linear equation in one variable with the help of Householder’s method and modified Newton’s method.

Maple implementation of the proposed algorithm is also discussed with sample computations. Couple of numerical examples are presented to illustrate and validation of the proposed method. Comparisons of the proposed method with existing methods are discussed and the results showed that the proposed algorithm required less number of iterations (see, for example, Table 1). As future work, one can use this algorithm for finding the approximate solution of the non-linear equations which have multiple solutions as well as for system of non-linear equations.

REFERENCES [1] A.S. Housholder, The Numerical Treatment of a Single Nonlinear Equation, McGraw-Hill, New York, 1970.

[2] C. Chun, ”Iterative methods improving Newton’s method by the decomposition method,” Comput. Math.

Appl. vol. 50, no. 10-12, pp. 1559–1568, 2005 [3] J.F. Traub, Iterative Methods for Solution of Equations, Prentice-Hall, Englewood Cliffs, NJ, 1964.

[4] J.F. Traub, Iterative Methods for the Solution of Equations (Englewood Cliffs, NJ: Prentice-Hall, 1964).

[5] J.H. He, ”A new iterative method for solving algebraic equations”, Applied Mathematics and Computation, vol. 135, no. 1, pp. 81–84, 2005.

[6] M.A. Noor, K.I. Noor, W.A. Khan, F. Ahmad, ”On iterative methods for nonlinear equations,” Applied Mathematics and Computation, vol. 183, no. 1, pp. 128–133, 2006.

[7] M.A. Noor, F. Ahmad, ”Numerical comparison of iterative methods for solving nonlinear equations,” Applied Mathematics and Computation, vol. 180, no. 1, pp. 167–172, 2006.

[8] M.A. Noor, K.I. Noor, ”Three-step iterative methods for nonlinear equations,” Applied Mathematics and Computation, vol. 183, no. 1, pp. 322–327, 2006.

[9] M. Saqib, M. Iqbal, S. Ali, T. Ismaeel, ”New fourth and fifth-order iterative methods for solving nonlinear equations,” Applied Mathematics, vol. 6, no. 8, pp. 1220–1227, 2015.

[10] Saied, Liao, ”A new modification of False-Position method based on homotopy analysis method,” Applied Mathematics and Mechanics, vol. 29, no. 2, 223–228, 2008.

[11] Sagralo, Mehlhorn, Computing real roots of real polynomials, 2013.

[12] S. Hussain, V. K. Srivastav, S. Thota, ”Assessment of Interpolation Methods for Solving the Real Life Problem,” International Journal of Mathematical Sciences and Applications, vol. 5, no. 1, pp. 91–95, 2015.

[13] S. Thota, V.K. Srivastav, ”Quadratically Convergent Algorithm for Computing Real Root of A numerical algorithm to find a root of non-linear equations...(Srinivasarao Thota)

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[14]

[15] [16] [17] [18] [19] [20] [21]

[22] [23] [24] [25] [26] [27] [28]

[29]

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Non-Linear Transcendental Equations,” BMC Research Notes, vol. 11, no. 909, pp. 1–6,2018, https://doi.org/10.1186/s13104-018-4008-z.

S. Thota, V.K. Srivastav, ”Interpolation based Hybrid Algorithm for Computing Real Root of Non-Linear Transcendental Functions,” International Journal of Mathematics and Computer Research, vol. 2, no. 11, pp. 729–735, 2014.

S. Thota, ”A New Root-Finding Algorithm Using Exponential Series,” Ural Mathematical Journal, vol.

5, no. 1, pp. 83–90, 2019.

S. Thota, T. Gemechu, ”A New Algorithm for Computing a root of Transcendental Equations Using Series Expansion,” Southeast Asian Journal of Sciences, vol. 7, no. 2, pp. 106–114, 2019.

T. Gemechu, S. Thota, ”On New Root Finding Algorithms for Solving Nonlinear Transcendental Equations,” International Journal of Chemistry, Mathematics and Physics, vol. 4, no. 2, pp. 18–24, 2020.

Sharma, J.R., Kumar, D, ”On a reduced cost derivative-free higher-order numerical algorithm for nonlinear systems,” Comp. Appl. Math. vol. 39, no. 202, 2020. https://doi.org/10.1007/s40314-020-01218-3.

Argyros IK, Hilout S. Numerical Methods in Nonlinear Analysis. World Scientific Publishing Company, New Jersey, 2013.

Constantinides A, Mostoufi N. Numerical Methods for Chemical Engineers with MATLAB Applications.

Prentice Hall PTR, New Jersey, 1999.

Moré JJ. A collection of nonlinear model problems. In, ”Allgower EL, Georg K (eds) Computational Solution of Nonlinear Systems of Equations Lectures in Applied Mathematics,” American Mathematical Society, Providence, RI, vol. 26, pp. 723–762, 1990.

Ortega JM, Rheinboldt WC. Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York, 1970.

Traub JF. Iterative Methods for the Solution of Equations. Chelsea Publishing Company, New York, 1982.

W.A. Khan, M.A. Noor, A. Rauf, ”Higher-order iterative methods by using Householder’s method for solving certain nonlinear equations,” Math. Sci. Lett. vol. 2, no. 2, pp. 107–120, 2013.

T.J. McDougall, S.J. Wotherspoon, ”A simple modification of Newton’s method to achieve convergence of order,” Journal of Applied and Mathematical letters, vol. 29, no. 1, pp. 20–25, 2014.

S.M. Kang, A. Rafiq, F. Ali, W Mahmood, ”A New Newton’s Type Method for Nonlinear Equations,” International Journal of Mathematical Analysis, vol. 10, no. 4, pp. 151–158, 2016.

A. Neamvonk, ”Three-Step Method For Finding Root of Non-Linear Equations,” IOSR Journal of Mathematics, vol. 15, no. 1, pp. 01–06, 2019.

T. Parveen, S. Singh, S. Thota, V. K. Srivastav, ”A New Hydride Root-Finding Algorithm for Transcendental Equations using Bisection, Regula-Falsi and Newton-Raphson methods,” National Conference on Sustainable & Recent Innovation in Science and Engineering (SUNRISE-19), (2019) (ISBN No. 978-935391-715-9).

V.K. Srivastav, S. Thota, M. Kumar, ”A New Trigonometrical Algorithm for Computing Real Root of Non-linear Transcendental Equations,” International Journal of Applied and Computational Mathematics,, vol. 5, no. 44, pp. 1-8, 2019.

BIOGRAPHIES OF AUTHORS Dr. Srinivasarao Thota (Corresponding Author) completed his M.Sc. in Mathematics from Indian Institute of Technology (IIT) Madras and Ph.D. in Mathematics from Motilal Nehru National Institute of Technology (NIT) Allahabad, India. Srinivasarao Thota’s areas of research interest are Computer Algebra (symbolic methods for differential equations), Numerical Analysis (root finding algorithms) and Mathematical Modelling (ecology). He has published his research work in several international journals and presented his work in different national and international conferences as oral presenter and expertise/invited presenter in different countries. Presently working at Department of Applied Mathematics, Adama Science and Technology University, Ethiopia. Further info on his homepage: https://srinivasaraothota.webs.com/

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International Journal of Advances in Applied Sciences (IJAAS) Vol. 10, No. 2, June 2021, pp. 149~155 ISSN: 2252-8814, DOI: 10.11591/ijaas.v10.i2.pp149-155

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Real power loss diminution by rain drop optimization algorithm Lenin Kanagasabai Department of EEE, Prasad V. Potluri Siddhartha Institute of Technology, Kanuru, Vijayawada, Andhra Pradesh, India

Article Info

ABSTRACT

Article history:

In this work Rain Drop Optimization (RDO) Algorithm is projected to reduce power loss. Proceedings of Rain drop have been imitated to model the RDO algorithm. Natural action of rain drop is flowing downwards form the peak and it may form small streams during the headway from the mountain or hill.

As by gravitation principle raindrop flow as stream then as river form the peak of mountains or hill then it reach the sea as global optimum. Proposed Rain Drop Optimization (RDO) Algorithm evaluated in IEEE 30, bus test system. Power loss reduction, voltage deviation minimization, and voltage stability improvement has been achieved.

Received Apr 29, 2020 Revised Mar 15, 2021 Accepted Apr 16, 2021 Keywords: Optimal reactive power Rain drop optimization algorithm Transmission loss

This is an open access article under the CC BY-SA license.

Corresponding Author: Lenin Kanagasabai Department of EEE Prasad V. Potluri Siddhartha Institute of Technology Kanuru, Vijayawada, Andhra Pradesh-520007, India Email: gklenin@gmail.com

1.

INTRODUCTION Real power loss reduction is main objective of this work. Various methods conventional [1]-[6] and Evolutionary techniques [7]-[19] are applied to solve the problem. Rain Drop Optimization (RDO) Algorithm applied to reduce the power loss. Rain drop actions have been imitated to model the algorithm. Natural behavior of rain drop is flowing downwards form the peak and it will form small streams during the progression from the hill. With reference to the gravitation the raindrop flow as stream then as river from the peak of mountains or hill then finally it reaches the sea. Reaching the sea by passing many areas including valleys is global optimum. Raindrops are engendered in arbitrary mode in the initial iteration itself, then each rain drop will assign a neighborhood by itself then in arbitrary mode neighbor points are produced. Projected algorithm begins with arbitrarily engendered solution afterwards exploration has been done sequentially around the present point until end of the end criterion and also revision of the present value will be there throughout the procedure. Rain Drop Optimization (RDO) Algorithm evaluated in standard IEEE 30, bus test system. Voltage deviation and power minimization achieved along with voltage enhancement.

2.

PROBLEM FORMULATION Solving the optimal reactive power dispatch (ORPD) problem plays a significant role in the efficient operation and planning of the power system. The aim of solving the ORPD is to determine the best operating point of system for maximizing the voltage stability, minimizing the system loss and the voltage deviations.

The best operating point includes the terminal voltages of the generators, taps of transformers and the injected reactive powers of the shunt compensators. The solution of the ORPD problem is formulated as an Journal homepage: http://ijaas.iaescore.com

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optimization problem applied for assigning set control parameters for a certain objective function, satisfying the operating constraints of the system.

Minimization F̃(x̅, y̅)

(1)

Subject to (2) E(x̅, y̅) = 0

(2)

I(x̅, y̅) = 0

(3)

x = [VG1 , . . , VGNg ; QC1 , . . , QCNc ; T1 , . . , TNT ]

(4)

y = [PGslack ; VL1 , . . , VLNLoad ; QG1 , . . , QGNg ; SL1 , . . , SLNT ]

(5)

Fitness function (F1 ) (6) is defined to diminish the power loss (MW), 2 2 F1 = PMin = Min [∑NTL m Gm [Vi + Vj − 2 ∗ Vi Vj cosØij ]]

(6)

Fitness function (F2 ) minimization of Voltage deviation is (7), 2

N

Ng

2

desired LB F2 = Min [∑i=1 |VLk − VLk | + ∑i=1|Q GK − QLim KG | ]

(7)

Fitness function (F3 ) (8) voltage stability index (L-index) is (9), (10), (11).

F3 = Min LMax

(8)

LMax = Max[Lj ]; j = 1; NLB

(9)

And {

Lj = 1 − ∑NPV i=1 Fji Fji =

Vi Vj

(10)

−[Y1 ]1 [Y2 ] V

LMax = Max [1 − [Y1 ]−1 [Y2 ] × i ] Vj

(11)

Equality constraints 0 = PGi − PDi − Vi ∑j∈NB Vj [Gij cos[Øi − Øj ] + Bij sin[Øi − Øj ]]

(12)

0 = QGi − QDi − Vi ∑j∈NB Vj [Gij sin[Øi − Øj ] + Bij cos[Øi − Øj ]]

(13)

Inequality constraints max min Pgslack ≤ Pgslack ≤ Pgslack

(14)

max Qmin gi ≤ Q gi ≤ Q gi , i ∈ Ng

(15)

VLmin ≤ VLi ≤ VLmax , i ∈ NL i i

(16)

Timin ≤ Ti ≤ Timax , i ∈ NT (17) Qmin ≤ Q c ≤ Qmax , i ∈ NC c C

(18)

|SLi | ≤ SLmax , i ∈ NTL i

(19)

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VGimin ≤ VGi ≤ VGimax , i ∈ Ng

151 (20)

Multi objective fitness is (21), (22), (23) 2

2

min min MOF = OF1 + xi OF2 + yOF3 = OF1 + [∑NL ] + ∑NG ] ] + xf OF3 i=1 xv [VLi − VLi i=1 xg [QGi − QGi

VLmin = i

VLmax , VLi > VLmax i i { min VLi , VLi < VLmin i

𝑄𝐺𝑖𝑚𝑎𝑥 , 𝑄𝐺𝑖 > 𝑄𝐺𝑖𝑚𝑎𝑥 𝑄𝐺𝑖𝑚𝑖𝑛 = { 𝑄𝐺𝑖𝑚𝑖𝑛 , 𝑄𝐺𝑖 < 𝑄𝐺𝑖𝑚𝑖𝑛

(21) (22)

(23)

3.

RAIN DROP OPTIMIZATION ALGORITHM Natural behavior of rain drop is flowing downwards form the peak and it will form small streams during the progression from the hill [20]. In the projected algorithm rain drops will be a particle in the population, and it has been described as (24), DP i = [Yi,1 , Yi,2 , Yi,3 , . . , Yi,k , . . , Yi,n ] i ∈ {1,2,3, . . , m}

(24)

DP i symbolize rain drop, number of variables indicated by “n” and Yi,k indicate the k th variable in the problem, size of the population is defined by “m”. DP i has been assumed as a vector or point in the “N” dimensional axis and through uniform distribution it has been engendered as function with constraints as (25).

Yi,k = uniform distribution function (UDF). (Lowerk , Upperk )

(25)

With radius “r” around the point of Rain Drop (RD) in the “N” dimensional axis with respect to the neighborhood value the change in Rain Drop (RD) value will be modernized. A Rain Drop (RD) “i” which possess a neighbor point “j” is indicated by NHPji as (26) and (27), ‖(RDi − NHPji ). unit vectork ‖ ≤ ‖radius(r). unit vectork ‖

(26)

raduis(r) = raduisinitial × f(iteration)

(27)

Naturally the dominant or main (M) neighbor point NHPMi satisfy amongst of all rain drop RDi and by objective function (F) the rain drop and neighbor point values are obtained by (28) and (29), F(NHPMi ) < 𝐹(RDi )

(28)

F(NHPMi ) < 𝐹(NHPji )

(29)

No main point for a single rain drop RDi then predominantly in the position of stationary. Then the rain drop has been take out of this situation through a procedure of explosion is defined by (30), NHPexploration = neighbor point × explosion base × explosion counter

(30)

The ranking of the rain drops in iteration’s is given by (31) and (32), D1it = F(RDi )|at t th iteration − F(RDi )|at 1st iteration

(31)

D2it = F(RDi )|at t th iteration

(32)

order(D1it ), order(D2it ); are orders at iteration t

(33)

ω1 , ω2 ; are weight cofficients and ranking it is rank of rain drop RDi Raindrops are engendered in arbitrary mode in the initial iteration itself, then each rain drop will assign a neighborhood by itself then in arbitrary mode neighbor points are produced. Throughout the procedure of the optimization the neighbor point will be within in the exploration space limits and if any engendered beyond the exploration space limit then it has been modernized by (34) and (35).

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if(NHPji ) < Lowerk then(NHPji ) = Lowerk

(34)

if(NHPji ) < Upperk then(NHPji ) = Upperrk

(35)

k

k

k

k

Subsequently for each rain drop and its neighbor points cost function will be computed then the comparison of values between rain drop and neighbor point will be done when there is dominant or main neighbor point found then the rain drop move towards to that point by altering its position. − Begin − Parameters values are engendered − Fix the each rain drop value as active − Rain drop’s initial population produced − Iteration =1 − Drop number =1 − Explosion counter =0 − Is rain drop is active? if yes got to next step or else go to step “o” − Engender the neighbor points − Rain drop and neighbor point cost function value computed − Change of rain drop position when a dominant neighbor point has been found then Explosion counter =0 then go to step “n” − Otherwise exploration process will be applied − Fix the rain drop as live − Swap the rain drop with dominant neighbor point − Drop number +1 − Is drop number <= number of population? If yes go to step “g” − Otherwise iteration +1 − Even after applying the exploration process no neighbor point found means then that particular rain drop is marked as motionless − After creation of the worth order list then lower order value rain drops are marked as motionless − Any live or active rain drop found ; Itertaion <= maximum itertaion − If yes go step “f” − Otherwise go to next step “w” − For all rain drops the cost function value will be computed − Discover the rain drop which possess the minimum cost functional value − Then optimal solution is the cost and raindrop position − End

4.

SIMULATION RESULTS Projected Rain Drop Optimization (RDO) Algorithm evaluated in standard IEEE 30 bus system [21]. Active and reactive power consumption is 2.8340 and 1.2620 per unit in 100 MVA base. Table 1 and Table 2 shows the parameters [21]; then Table 3 to Table 4 shows the comparison results. Figures 1-4 gives the graphical comparison.

Table 1. Variables System [21]

Variables VG Tt VAR

Minimum (PU) 0.950 0.90 0.0

Maximum (PU) 1.10 1.10 5 .0

Table 2. System parameters Description [21] NB NG NT NQ NE Power loss Base casee for VD (Per Uit)

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Table 3. Power loss comparison with different metaheuristicalgorithms Power Loss (MW) Voltage .D (PU) L-index (PU)

DE[22] 4.555 1.9589 0.55130

GSA[23] 4.5143 0.87522 0.141090

APO-PSO [24] 4.398 1.047 0.12670

RDO 0.940 4.226 1.044

Table 4. Comparison with reference to voltage stability improvement Power loss(MW) Volatge D (PU) L-index (PU)

DE[22] 6.4755 0.0911 0.143520

GSA[23] 6.9117 0.0676 0.13490

APO-PSO [24] 5.698 0.087 0.13770

RDO 5.429 0.083 0.1314

Table 5. Comparison with reference to voltage deviation minimization Power loss (MW) Volatge. D (PU) L-index (PU)

DE[22] 7.0733 1.419 0.12460

GSA[23] 4.9752 0.21579 0.136840

APO-PSO [24] 4.478 1.8579 0.12270

RDO 4.249 1.8205 0.1173

Table 6. Comparison of values with reference to multi objective formulation Power Loss (MW) Volatge .D (PU) L-index (PU)

APO-PSO [24] 4.842 1.009 0.1192

RDO 4.738 1.003 0.1184

Figure 1. Comparison of power loss

Figure 2. Comparison with respect to VSI

Figure 3. Comparison of loss with reference with VDM

Figure 4. Comparison of loss with reference with MOF

5.

CONCLUSION In this work optimal reactive power dispatch problem has been successfully solved by Rain Drop Optimization (RDO) Algorithm. Projected algorithm begins with arbitrarily engendered solution afterwards exploration has been done sequentially around the present point until end of the end criterion and also Real power loss diminution by rain drop optimization algorithm (Lenin Kanagasabai)

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revision of the present value will be there throughout the procedure. Throughout the procedure of the optimization the neighbor point will be within in the exploration space limits and if any engendered beyond the exploration space limit then it has been modernized. Rain Drop Optimization (RDO) Algorithm evaluated in IEEE 30, bus test system. Voltage stability enhanced, power loss reduced with voltage deviation minimization.

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BIOGRAPHY OF AUTHOR Lenin Kanagasabai has received his B.E., Degree in Electrical and Electronics Engineering from University of Madras, M.E., Degree in Power Systems from Annamalai University and completed PhD in Electrical Engineering from Jawaharlal Nehru Technological University Hyderabad, India. He published more than 300 international journal research papers and presently working as Professor in Prasad V. Potluri Siddhartha Institute of Technology, Kanuru, Vijayawada, Andhra Pradesh -520007.

Real power loss diminution by rain drop optimization algorithm (Lenin Kanagasabai)

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Groundwater suitability for irrigated agriculture in Alluvial Bengal delta plain: A review Md. Shajedul Islam, M. G. Mostafa Institute of Environmental Science, University of Rajshahi, Rajshahi, Bangladesh

Article Info

ABSTRACT

Article history:

Groundwater is a vital source of irrigation and domestic purposes in Bangladesh, and hence, it must satisfy the water quality guidelines.

The study has selected eleven (11) Districts of Bangladesh and collect secondary data regarding the irrigation water quality of groundwater. Several irrigation water indices, such as soluble sodium percentage (SSP), sodium adsorption ratio (SAR), magnesium adsorption ratio (MAR), residual sodium carbonate (RSC), Kelly’s ratio (KR), permeability index (PI), and irrigation water quality (IWQ) index are applied to evaluate irrigation water quality.

According to IWQindex, the results showed 25.5% of water samples fell in highly suitability water type, whereas 33.5% exhibited low suitability type, and the remaining 41% were showed medium suitability for irrigation purposes. The values of SAR, SSP, RSBC, and MAR indices showed that about 31-64% of water samples were very good, whereas 5-20% were very poor for the same purpose. The results of TDS, EC, and total hardness showed good results as 8893% of water samples fell in fair to excellent quality. The salinity hazard was found in the groundwater of coastal areas and completely unfit for irrigation. The study findings would help for improving the management of the groundwater resources for agricultural purposes in Bangladesh.

Received Oct 12, 2020 Revised Jan 23, 2021 Accepted Feb 3, 2021 Keywords: Bengal basin BGM delta Irrigation groundwater quality IWQ index Salinity hazard Soil permeability

This is an open access article under the CC BY-SA license.

Corresponding Author: M. G. Mostafa Institute of Environmental Science University of Rajshahi Rajshahi 6205, Bangladesh Email: mgmostafa@ru.ac.bd

1.

INTRODUCTION Bengal delta basin (BDB) is covered by alluvial sedimentary soil with enough thick deposited by the Ganges, Brahmaputra, and Meghna (GBM) rivers. It is one of the biggest deltas and widespread fertile cultivable land in the world [1]. Two Himalayan rivers the Ganges and the Brahmaputra are both fall to the Bay of Bengal as a collective river transport the largest sediment load. These two rivers join central Bangladesh with the Meghna, a non-Himalayan river that creates the largest delta in the world named the Bengal delta. This delta is one of the most widespread alluvial or sediment basins and establishes the delta plain and the lowers floodplain deposits of Bangladeshis at the mouth of the Ganga–Brahmaputra–Meghna Journal homepage: http://ijaas.iaescore.com

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(GBM) river systems. The Ganga–Brahmaputra river systems together carry the largest sediment load of the world, which transport about 80% of the sediment load during the rainy season [2]. More than 200 rivers and streams run through Bangladesh, with a mean annual discharge of water of about 38,000 m3/s [3], carrying over 2.4×109 MT of sediments every year before discharging lastly into the Bay of Bengal [4]. The huge alluvial sediments washed away and deposited in basin areas and finally, made it a bigger arable region in the world. Bangladesh is a densely populated (2890/mile2, which ranks 10th in the world) and agrarian country Figure 1. Almost 90% of its lands are cultivable and 55% of the inhabitant are engaged in the agricultural sector [5]. This sector plays a vital role in the country's economy, which accounts for about 21% of involvement in countrywide GDP [5]. Nevertheless, still now, agriculture is being conducted in nonsustainable, unplanned, and unsystematic ways. Besides, due to the geogenic and anthropogenic causes, the quality of irrigation water deteriorates progressively, which affects the soil environment and crop production.

Figure 1. Administrative map of Bangladesh In Bangladesh (BDB), before the 1970s, agriculture was completely dependent on surface water and seasonal monsoon rainfall [6]. Later that time to harvest high-yielding rice varieties and to attain success the global campaign of clean and fresh drinking water decade (1980–1990), millions of drinking and irrigation shallow and deep-water wells have installed in Bangladesh [7]-[9]. Now a day, rather than surface water, groundwater is the main source of irrigation in the country [10]. By 2006, almost 78% of the irrigated paddyfields were supplied by groundwater of which nearly 80% of the irrigation water derived from shallow (25-40 m) engine tube-wells, and the rest was irrigated by deep (100-150 m) tube-wells [11], [12]. Such irrigation water desires to be of suitable quality. The chemical characteristics of irrigation water can affect plant growth and crop quality directly through nutrients deficiency or toxicity, or indirectly by the degradation of soil quality [13]. The bad quality irrigation water reduces the soil productivity as well as changes in soil physical and chemical properties. It also creates crop toxicity and ultimately reduces the yield of the crop [14], [15]. Now a day, arsenic contamination is a threat to irrigation water. Besides, presently groundwater is considered to be the only resource for irrigation water supply in the country. Therefore, its rational use should ensure in terms of both quality and quantity [16]. So, information regarding irrigation water quality is imperative to understand the necessity of agro-management for long-term productivity [17].

Agricultural development, land use and crop diversity, rapid urbanization and industrialization, and anthropogenic pollution have direct or indirect impacts on groundwater quality. Irrigated agriculture mostly depends on groundwater resources worldwide [18]. The situation in Bangladesh concerning water distribution for irrigation is similar to other lower-middle-income countries in the world [19]. Unfortunately, in the recent past decade, irrigation groundwater use by open canals has caused a rapid decline in water Groundwater suitability for irrigated agriculture in alluvial Bengal delta…, (Md. Shajedul Islam)

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reserves and levels in many regions of Bangladesh [20]. Groundwater resource is vulnerable not only the overexploitation during irrigation, but also geogenic and anthropogenic contamination. Quality of water is vital for each type of cultivation since poor quality irrigation water may lead to a huge economic loss and a reduction in crop production. Besides, long-term agricultural productivity can sustain if irrigation water quality is properly monitored [21]. So, the irrigation water quality might be influenced by the concentrations of various physiochemical parameters dissolved in water resulting from water-rock interactions and anthropogenic activities.

Many investigators revealed the groundwater quality of different districts of Bangladesh for irrigation purpose, and they were: Mridha [22] explored groundwater at Natore district, Faridpur district’s groundwater investigated by Islam [23], Quddus and Zaman [24] studied the irrigation water quality of some selected villages of Meherpur district, Talukder [25] conducted an extensive study on groundwater of Kishoreganj district, Sarkar and Hassan [16] assessed the groundwater of Pabna district for irrigation, Shahidullah [26] and Sultana [27] investigated the groundwater quality in Mymensingh and Khulna districts, respectively. Raihan and Alam [28] analyzed groundwater quality throughout the Sunamganj district, Islam and Shamsad [29] assessed groundwater quality of Bogra district, and Rahman [30] studied groundwater quality of Satkhira district for irrigation purpose. A study on groundwater illustrated that the groundwater in coastal areas was not suitable for irrigation purposes in the pre-monsoon season. However, it was found suitable for the monsoon and post-monsoon seasons [31].

Quite a lot of irrigation water quality indexes are usually followed to assess water quality in literature. Indeed, irrigation water quality (IWQ) indexes are expected to deliver a simple tool for water managers and policymakers on the quality and potential uses of a given aquifer system. At first, Horton [32] proposed an integrated WQIs for assessing water quality. Since then, many water quality indices reported by several investigators worldwide [e.g., 19, 33-37], for example, Simsek and Gunduz [38] have developed a GIS-based irrigation water quality (IWQ) index by combining well-known hydrochemical parameters (TDS, EC, RSC, SAR, and others) to assess the irrigation water quality of the Simav Plain in Turkey. Ashraf [39] developed a GIS-based irrigation water index for calculating SAR, RSC, or SSP with other parameters.

Romanelli et al. (2012) assessed groundwater quality for suitability of irrigation purposes using the IWQ index [40]. The index integrated the hydro-chemical, hydrogeological, and topographic parameters (EC, SAR, RSC, slops, hydraulic gradient, and aquifer thickness). In this paper, we try to assess the countrywide irrigation groundwater quality through the calculation of various parameters such as Soluble Sodium Percentage (SSP), Residual Sodium bicarbonate ( RSC), Kelley’s Ratio (KR), Permeability Index (PI), and Magnesium Adsorption Ratio (MAR). Thus, the study aimed to assess the suitability of irrigation water in Bangladesh using several indices. Besides, countrywide soil permeability, hydraulic conductivity of soil, soil class. Also assessed by this study. However, the results of this study provide a guideline for an agricultural manager, hydrologist, policymakers, and water planner of a certain aquifer system to take a suitable initiative for groundwater quality management in the selected region.

2. STUDY AREA-GEOMORPHOLOGY, HYDROLOGY, AND WATER TYPE 2.1. Geomorphology The chemistry of groundwater typically depends on the local geological setting in aquifers. In this section, we draw a picture briefly of the aquifer geomorphology of Bangladesh. There are four major physiographic regions, i.e., (Ⅰ) Pleistocene courtyard in the Barind and Madhupur zones (Ⅱ) tertiary alluvial in the eastern and northern hills (Ⅲ) the delta covers the rest of the country, and (Ⅳ) Holocene (recent) floodplains of the Ganges, Brahmaputra, and Meghna (GBM) river exist at the surface in the country [41], [42]. The hydrogeological cross-sectional view of Bangladesh from north to the south showing the aquifer system and groundwater flow outline shown in Figure 2. Historically, around 6,000 years ago the sea level was much lower, and the main rivers divided deep channels surrounding the Barind and Madhupur tract zone [43]. With some Pleistocene terraces, deltaic flood plains comprise the main portion of the basin and its sediments consist mostly of unconsolidated deltaic deposits and alluvial except for the mixed geology zone of pre-quaternary deposits that cover the north-eastern and southeastern mountainous areas of Bangladesh.

Collected with the tertiary alluvial arrangements the maximum depth of the layout is mostly 20 km [44]. The country has promising hydrogeologic conditions and tropical monsoon weather indicates possible storing of groundwater in the aquifers. The uncombined nearby-surface Pleistocene to recent estuarine and fluvial sediments underlying most of the country usually form productive aquifers. Deep semi-contracted to the uncontracted fluvial-deltaic deposit of Miocene age to the recent forms of many aquifers. But excluding the Dupi Tila sandstone construction of the plio-Pleistocene stage, others are too deep to consider for groundwater withdrawal except in the mountainous region (18% of total areas) [43]. Most of the groundwater extraction for irrigation or domestic purposes in the Barind and Madhupur upland areas are from the Dupi Int J Adv Appl Sci, Vol. 10, No. 2, June 2021: 156 – 170

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Tila aquifers. The floodplains of the active/inactive delta plain and the major rivers of the GBM delta complex occupies about 82% of the country area [7]. The geological studies indicated that the bulk of the best aquifers occurs from 30 to 130 m depth [41]. These alluvial deposits are cyclic sediment of typically medium to fine sand, clay, silt, and siltstone. The separate layers cannot trace for long distances, vertically or horizontally [7], [45].

Rain and floodwater are the principal sources of groundwater recharge in Bangladesh. Numbers of studies forecast that vast groundwater-fed irrigation would prolong net recharge in areas where soil properties and surface lithology are good permeable that favor recharge [6], [46], [47]. The study projected area wise annual usable and potential recharge between 183 to 1287 mm and 135 to 1910 mm, respectively. The approximations of net recharge in Bangladesh have increased from 132 mm/yr over a period from 1975 to 1980 to about 190 mm/yr for the period of 2002 to 2007 [47]. Recent past studies confirmed that the ratio of groundwater recharge and abstraction in the country gradually downfall.

Figure 2. Map of Bengal delta plain (BDP) 2.2. Hydrogeology Very productive aquifers occur underneath both the Pleistocene terraces and Holocene floodplains, the shallowest usually encountered within 15 to 45 m of the surface. In Bangladesh, most shallow irrigation water wells are less than 50 m deep. Generally, 50–75% of the sequence can effectively develop to this depth [46]. Saline groundwater is present in parts of the coastal area and some inland zones [48]. In the coastal zones, freshwater aquifers are encountered either within the first 20 m or below about 100–150 m depth. An equal deeper aquifer is also exploited at some towns in the north of the coastal zone [49], following an aquitard, which is present in places but seems not to be locally extensive.

2.3. Water quality In the region of BDP, before the detection of arsenic contamination, the physio-chemical quality of groundwater underneath the Holocene flood plains was thought to be commonly good, although the shallow groundwater is vulnerable to contamination by some essential and non-essential metals and microbes [50].

Calcium and iron were known as an extensive nuisance, and saltiness a constraint in the shallow layer of the coastal area. Besides, arsenic, the Department of Public Health Engineering (DPHE) identified Mn and B as common, naturally occurring ingredients, present in places above the WHO guidelines for potable water (0.5 mg/l in both cases) [49]. But these elements are good for irrigation water. The groundwater type of Bangladesh is mostly Ca-Mg-HCO3 accomplished with high minerals (EC: 500–2000 µS/cm) and Na-Cl type water adjacent to the coastal areas. This contrasts with groundwater from the sandy aquifer of Dupi Tila underneath the Pleistocene, which is generally of the Na-HCO3 type and has fewer minerals (EC: 300–600 µS/cm) [50]. Groundwater underneath the Holocene flood plains in the country is considered by high bicarbonate loads, with HCO3- usually present in more than a hundred mg/L. It is mostly anoxic and Groundwater suitability for irrigated agriculture in alluvial Bengal delta…, (Md. Shajedul Islam)

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mostly has a strongly reducing environment, nearby to the extent of methanogenesis [51]. In this area, arsenic concentration is very high (50-1000 µg/L) combined with a high dissolved iron present at a range of 5-10 mg/L. Manganese usually exceeds 0.5 mg/l. Nitrate and Sulphate concentration is normally low below the Holocene floodplains, mostly less than about 5 mg/L [52], [53]. These chemical characteristics reflect the conditions of groundwater quality as well as irrigation water quality.

3.

METHODS AND MATERIALS Though out the review process, we used secondary data from several published articles and reports.

This study searched Google Scholar, Scopus, Web of Science, PubMed, and other databases for publications across 25 years and dated 1995 to 2020. The following terms were searched using the Boolean Operators ‘and’ and ‘or’: (a) Bengal delta plain, (b) geochemistry of groundwater in Bangladesh, (c) irrigation water quality, (d) IWQ index, (e) geological formation of Bengal basin, (f) water class. Primarily, we were identified over 150 published papers and reports, but finally included 120 articles in the high impact journal.

Here, we follow the PRISMA Statement for every event of inclusion and exclusion criteria. Extracted data are included in a Table and assessed the irrigation water quality, soil permeability, and soil class of Bangladesh through the Table. For these purposes, various well-recognized indexes and theories for irrigation water quality evolution were used.

3.1. Irrigation water quality index (IWQindex) The IWQ index is prepared based on the linear correlation of four sets of irrigation water quality parameters that are connected to form a single index value to assess the irrigation water quality in Bangladesh. According to the guiding principle offered by Ayers and Westcot [33], four categories of irrigation water quality parameters, for instance, definite ion toxicity, permeability hazard, salinity threat, and associated effect are designated Table 1. Simsek and Gunduz [38] were designated detailed standard measures for irrigation water quality indexes. All parameters are given a weight factor Table 2 & Table 3 from the 4 (highest) and 1 (lowest) points in the method. Among those 4 factors, salinity peril is the most vital factor, and the highest priority (weight = 4), whereas the associated effects on sensitive crops are the least significant factor in the assessment of irrigation water quality. The rest of the two parameters such as permeability hazard and definite ion toxicity rated in declining order along with importance for irrigating water quality. The irrigation water quality index is measured by the using as (1) & (2); 𝐼𝑊𝑄𝑖𝑛𝑑𝑒𝑥 = ∑4𝑖=1 𝐺𝑖

(1)

Where, i = incremental index, and G = contribution of each one of the four hazard groups that are vital to assess the quality of specific irrigation water resource; and G can be calculated by the; 𝐺=

𝑤 𝑁

∑𝑁 𝑘=1(𝑟𝑘 )

(2)

Here, k = incremental index; N = total number of parameters for the analysis; w = weight value of the category; and r = rating value of individually parameter as given in Table 2 and Table 3.

Table 1. Classification of irrigation water quality standards (according to, ayers and westcot [33]).

Potential problem in irrigation Salinity (effects water availability for crop)

Permeability (effects rate of water infiltration into soil)

Specific ions toxicity (effects sensitive type crops)

Miscellaneous effects (effects vulnerable crops)

Parameters

Units

Grade of restriction on use Slight to moderate Severe 450–2000 > 2000

TDS

mg/L

None < 450

EC

μS/cm

< 700

700–3000

> 3000

SAR = 0–3

%

EC: > 700

700–200

< 200

SAR = 3–6 SAR = 6–12 SAR = 12–20 SAR = 20–40 Sodium

% % % % mEq/L

EC: > 1200 EC: > 1900 EC: > 2900 EC: > 5000 < 3.0

1200–300 1900–500 2900–1300 5000–2900 3.0–9.0

< 300 < 500 < 1300 < 2900 > 9.0

Boron Chloride Bicarbonate

mg/L mg/L mg/L

< 0.7 < 140 < 90

0.7–3.0 140–350 90–500

> 3.0 > 350 > 500

pH

–

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Normal range: 6.5–8.4

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Table 2. Cataloguing for IWQ index parameters (according to, ayers and westcot [33]).

Hazard Salinity hazard

Weight 4

Parameter Electrical conductivity (μS/cm)

Total dissolved solids (mg/L)

Permeability and Infiltration hazard

3

See Tab. 4 and 5a for details

Specific ion toxicity

2

Sodium adsorption ratio (%)

Boron (mg/L)

Chloride (mg/L)

Assorted effects to sensitive crop

1

Bicarbonate (mg/L)

pH

Range EC < 700

Rating 3

Suitability High

700 ≤ EC ≤ 3000 EC > 3000 TDS < 450

2 1 3

Medium Low High

450 ≤ TDS ≤ 2000 TDS > 2000

2 1

Medium Low

SAR < 3.0

3

High

3.0 ≤ SAR ≤ 9.0 SAR > 9.0 B < 0.7 0.7 ≤ B ≤ 3.0 B > 3.0 Cl < 140 140 ≤ Cl ≤ 350 Cl > 350 HCO3 < 90

2 1 3 2 1 3 2 1 3

Medium Low High Medium Low High Medium Low High

90 ≤ HCO3 ≤ 500 HCO3 > 500 7.0 ≤ pH ≤ 8.0 6.5 ≤ pH < 7.0 and 8.0 < pH ≤ 8.5 pH < 6.5 or pH > 8.5

2 1 3 2

Medium Low High Medium

1

Low

Table 3. Classification for infiltration and permeability hazard

EC

<3 > 700 700–200 < 200

3–6 > 1200 1200–300 < 300

SAR (%) 6–12 12–20 > 1900 > 2900 1900–500 2900–1300 < 500 < 1300

Rating > 20 > 5000 5000–2900 < 2900

3 2 1

Suitability High Medium Low

3.2. Methods for hydrogeochemical and water quality evaluation In the agricultural sector, utilization of bad water quality can make four types of problems such as toxicity hazard, water impermeability, salinity hazard, and miscellaneous [33]. Water quality assessment of irrigation, there are four most common criteria like EC or TDS; residual sodium carbonate (RSC); sodium adsorption ratio (SAR); concentration of some ions like Na +, HCO3-/CO32-, and Cl- [54], [55]. For the present irrigation water quality assessment besides the separate chemical parameters, the following parameters have been considered. To assess countrywide water quality for irrigation the following parameters were calculated and the results are included in Table 5 and Table 6: a.

The total hardness (TH) in ppm [55]-[57] was determined by as (3); 𝑇𝐻 = 2.497𝐶𝑎2+ + 4.115𝑀𝑔2+

b.

(3)

To assess the water quality for irrigation, the alkali or sodium hazard stated by the sodium adsorption ratio (SAR) is extensively used [19], [58]. If water samples with high Na + and low Ca2+ concentration, the ion exchange complex may become saturated with Na + which abolishes the soil architecture [56].

The SAR value of irrigation water calculates the relative proportion of Na + to Ca2+ and Mg2+ [59], and According to Richards [60], sodium adsorption ratio (SAR) is expressed as (4). 𝑆𝐴𝑅 =

𝑁𝑎 + √(𝐶𝑎2+ + 𝑀𝑔2+ )/2

(4)

Where, Na+, Ca2+ and Mg2+ are expressed as the concentrations (mEq/L) of Na, Ca, and Mg ions in water, respectively [33].

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Soluble sodium percentage (SSP) or %Na was used to evaluate the sodium hazard in irrigation water.

Todd [56] established SSP or %Na as (5): 𝑆𝑆𝑃 𝑜𝑟 %𝑁𝑎 =

d.

(𝑁+ +𝐾 +)×100 (𝐶𝑎2+ +𝑀𝑔2+ +𝑁𝑎 + + 𝐾 +)

The residual sodium carbonate (RSC) is calculated taking the alkaline earths (Ca and Mg) and weak acids (H2CO3) as (6) [55], [61]: 𝑆𝐶 = (𝐶𝑂3 2− + 𝐻𝐶𝑂3 − ) − (𝐶𝑎2+ + 𝑀𝑔2+ )

e.

𝑁𝑎 + √𝐻𝐶𝑂3

−

(𝑁𝑎 ++𝐶𝑎2+ +𝑀𝑔2+)

× 100

(8)

Magnesium adsorption ratio (MAR) also recognized as magnesium hazard was calculated [55] as (9): 𝑀𝐴𝑅 =

h.

(7)

Doneen [63] defined permeability index (PI) as (8): 𝑃𝐼 =

g.

(6)

Gupta [62] expressed residual sodium bicarbonate (RSBC) as (7): 𝑆𝐵𝐶 = 𝐻𝐶𝑂3 − − 𝐶𝑎2+

f.

(5)

(𝑀𝑔2+ ×100) (𝐶𝑎2+ +𝑀𝑔2+ )

(9)

Lastly, Kelley’s ratio (KR) [64] described as (10) 𝐾𝑅 =

𝑁𝑎 + (𝐶𝑎2++𝑀𝑔2+ )

(10)

All ionic parameter concentrations are in mEq/L. All these parameters and individual physicochemical parameters have compared with national and international standards to assess the groundwater suitability for irrigation. The values of all the above parameters of countrywide groundwater samples are reported in Table 5 and Table 6.

4.

RESULTS AND DISCUSSION In Bangladesh, groundwater is the main source of irrigation, which is around 30 to 40% of net tillable land [10], [65]. The groundwater contribution to the whole irrigated zone increased expressively from 41% in 1983 to 86% in 2002 [66]-[68]. Several studies illustrated that the overexploitation of groundwater and other anthropogenic activities are the cause of groundwater level and quality degradation. The water class used for irrigation is vital for the yield and number of crops, protection of the hydrological environment, and preservation of soil productivity. The physical and mechanical properties of the soil, soil permeability, and ex. soil structure (aggregational stability) are very sensorial to the type of transferable chemical constituent present in irrigation water.

The pH, Na hazard, salinity hazard, some trace elements, bicarbonate, and carbonate in connection with the Mg and Ca content, toxic anion, free Cl, and nutrients are the most crucial factors to regulate the suitability of water use in irrigation [69]. Besides, according to Michael [54], Raghunath [55], Matthess [70], and Guy [71] the agriculture water quality is decided by the 4 most admissible criteria such as TDS or EC, the level of certain specific elements like Na, K, Mg, Ca, Cl and/ or Br contents; the relative quantity of Na to other cation, denoted by Sodium Adsorption Ratio (SAR); and Residual Sodium Carbonate and Bicarbonate (RSC & RSBC). Apart from these, other measures like the presence of soil hardpan, the depth of the water layer, CaCO3 level in the soil, K and NO3 ions have influenced the appropriateness of irrigation water indirectly [54]. Besides, Matthess [70] and Ayers and Westcot [33] described that poor-quality irrigation water creates 4 types of problems; specific ion toxicity (affects sensitive crops), salinity (effects crop water availability), water permeability (effects penetration rate of water into the soil), and miscellaneous [71], [72].

The values of including previously discussed parameters, other parameters such as Soluble Sodium Percentage (SSP), Residual Sodium bicarbonate (RSC), Kelley’s Ratio (KR), Permeability Index (PI), and Magnesium Adsorption Ratio (MAR) of countrywide irrigation groundwater samples have included in Int J Adv Appl Sci, Vol. 10, No. 2, June 2021: 156 – 170

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Table 5. Also, the limits of some important indices for rating water quality and its suitability for irrigation purposes are presented in Table 4.

Table 4. Limits of important parameter indices for rating groundwater quality for irrigation use Category (Water class) Ⅰ Ⅱ

EC, (µS/cm) <700 700-3000

SAR (%) <10 10-18

Irrigation water quality indices SSP RSC PI MAR (%) (me/L) (me/L) (%) <20 >75 20-40 ˂1.25 25˂50 75 40-80 1.25-2.5 ˂25 -

Ⅲ

>3000

18-26

Ⅳ

-

>26

>80

>2.5

-

Ref.

UCCC [73]

Fipps [71]

Wilcox [74]

Gupta and Gupta [62]

Hem [57]

TDS (mg/L) >2000

Salinity (mg/L) ˂450 450-2000

-

4502000 ˂450

Gupta and Gupta [62]

Bauder [17]

UCCC [73]

>2000

Degree on restriction on use Excellent Good Fair Poor or Rejection

The TH, TDS, and EC pooled value of groundwater of 11 different Districts of Bangladesh are presented in Table 6. Several reports showed that the salinity intrusion in the coastal groundwater of Bangladesh makes it unfit for irrigation purposes [16], [30], [31], [72], [75]-[77]. Again, most shallow aquifer’s water, including the coastal region, of 60 districts out of 64 contaminated with arsenic [7], [78] and that used for irrigation. It has been estimated that yearly arsenic input with irrigation water is around 4.4 kg/ha in the paddy field [79] and in rice grains, arsenic is found above 0.017 mg/gm [80]. EC and TDS are significant in considering the irrigation water quality as various toxic solid materials may embed in the water, which causes damaging the plants [70]. Regarding the degree of restriction use, TDS concentration <450, 450-2000, and >2000 mg/L represent the agriculture water as ‘none’, ‘slight to moderate’, and ‘severe’ respectively which are presented in Table 4 [73]. According to the water quality indices, the south zone is classified as ‘slight to moderate’ and ‘severe’ and both north and center areas as ‘none’ and ‘slight to moderate.

Salinity is the dissolved salt content of a water body. It is used to designate the levels of dissimilar salts such as NaCl, MgSO4, CaSO4, and bicarbonates. The concentration of chlorine is straight proportional to salinity, which creates from the dissociation of various chlorinated. Besides, Na and TDS are other very significant parameters that can use to detect the influence of groundwater salinity and major component loads. Dider-Ul reported that in the case of groundwater of Khulna district, Na + and Cl- are strongly positively correlated with TDS (r = 0.87 and 0.89 respectively) [81]. They also stated that all others parameters i.e., Na+ Ca++, Mg++ and K+ also well correlated with Cl- (r=0.90, 0.88, 0.87 and 0.0.76 respectively) so, they originated from the same sources. A countrywide study showed that According to WHO classification of groundwater based on TDS, 12% of the sample fall in excellent, 23% are good, 46% are fair, 07% poor, and 12% falls in the unacceptable category Figure 3 [82].

The values of all irrigation water quality parameters are shown in Figure 4 and Table 5 and Table 6.

Box plot indicates that the EC value is twice than TH value in most of the sampling sites Figure 4. In the coastal areas, the EC, as well as TDS values, are very high rather than the other part of the country. The higher value of EC and TH in the groundwater samples pose a threat to crop production in the study area.

RSBC and RSC values of the countrywide groundwater are almost the same, indicating the higher value of Ca and HCO3-. The SAR, SSP, PI, MAR, and KI values are shown in the box plot. The box plots Figure 4 show that the assessment of mean, median, minimum, and maximum values of SAR, SSP, and Na% indicate similar values in the studied samples.

EC and total hardness are the important parameters that are related to groundwater salinity and freshness. According to WHO [82] salinity hazard based on EC value has been classified into four groups; low salinity hazard, medium salinity hazard, high salinity hazard, and very high salinity hazard. Wilcox drew the classification of EC as excellent, good, fair, and poor categories. The study showed that about 12, 53, 25, and 10% of water fell into excellent, good, fair, and poor categories, respectively Figure 3 [74]. The spatial distribution of groundwater showed the high EC values range from 2000 to 5000 µS/cm in the coastal region of Bangladesh [ref. 23: Khulna district; 84: Sathkhira district; 72: Patuakhali district]. In contrast, hardness is an important parameter for determining the suitability of groundwater for domestic, industrial, and agricultural uses [92]. It is defined as the sum of the concentration of their ion expressed in mg/L of CaCO3.

The classification of the groundwater based on hardness is presented in Figure 3 [93]. Accordingly, 62% of samples are soft and 8% fall in the very hard category.

The value of irrigation water quality parameters such as SAR, SSP, RSC, RSBC, MAR, and KR of 11 different Districts in Bangladesh are shown in Table 5. Water permeability of soil is an important factor in Groundwater suitability for irrigated agriculture in alluvial Bengal delta…, (Md. Shajedul Islam)

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the fertility rate of cultivable land. Permeability problem occurred when the usual percolation rate of soil significantly reduced and hampers moisture supply to crops, which is accountable for the two most water quality factors as the salinity of water and its Na content relative to Ca and Mg [16]. High salinity increases permeability rate in water and low salinity or water with high a Na to Ca ratio (Na: Ca) decreases infiltration [33]. Balance of some cations and anions or comparative proportions of other different cations well-defined

by SAR, SSP, RSC, RSBC, MAR, KR. are also indicators of infiltration problems. A large proportion of Na in soil with chloride and carbonate or sulfate named saline or alkali soils, respectively [30. 56]. Percent of Na (SSP) in water reacts with soil to decrease soil permeability and its frequent use makes the soil impermeable, whereas high Na leads to grow of alkali soil [55]. High Na saturation also causes Ca deficiency. In contrast, the presence of Ca and/or Mg salt in irrigation water checks the bad effects of Na by increasing the permeability of the soil [94]. Figure 5 shows that concerning SAR, SSP, RSBC, and MRI 31-64% of water samples are very good in position, whereas 5-20% are very poor or rejected for the uses of irrigation purposes.

Figure 3. Countrywide (selected 11 Districts) EC, TDS, and total hardness status of groundwater

Besides, saltwater dissolves and leaches most of the soluble minerals, including Ca and Mg from the topsoil [33]. Sodium content, compare to Ca and Mg load, usually known as SAR impacts the penetration rate of water and so, low SAR is at all times desirable. In the maximum samples, SAR values ranged below 1 and classified as excellent according to the conditions set by UCCC except for the coastal areas [73] and Todd [56], which showed in Table 5. Hence, rendering to SAR, the groundwater tested was suitable for crop production. Besides, the PI value of water with 75% or more (>75%) and KR value with less than 1 (˂1) are suitable for irrigation. Table 5 shows that the PI and KR values are good in the position except in the coastal areas. Concerning, Mg: Ca and Na: Ca values, maximum water samples have good permeability characteristics and the information on Hazard Classes are almost acceptable for irrigation Table 6. The samples of the coastal region (Khulna, Satkhira, and Patuakhali) are determined as high salinity (C3) and high/medium sodium hazard (S2 or S2) i.e., the hazard classes are C3S2, C2S2, or C2S3 Table 6. The suitability analysis and the total value of the index of irrigation water quality are presented in Table 7. The values given in the Table are obtained by assigning different rating factors (i.e., 1, 2, and 3) to each parameter without changing its weighting coefficient Table 2, thus yielding three different index values (i.e., 45, 30, and 15). The medians of these values are used to set the upper and lower limits used in each class quantified in Table 7.

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Table 5. Irrigational groundwater quality of Bangladesh (11 selected District) on different quality indices.

Sampling Area

Irrigational water quality indices (mean value) and degree of water quality* SAR SSP RSBC RSC PI MAR KR (%) (me/L) (me/L) (Me/L) (%) (%)

Source

Shahidullah [26] 0.41 13.4 0.44 Fulpur, M’singh Dist.

Sarkar [16] 0.63 28.5 4.47 3.71 73 17.54 0.22 Pabna district Tanvir [83] 5.66 55.91 1.18 80 18.29 1.59 Satkhira Dist.

Prodip [84] 2.40 44.14 0.81 58.97 0.74 Comilla District Didar-Ul [81] 12.64 71.37 3.29 54.78 6.82 Botiaghata, Khulna Dist Atikul [72] 10.9 61.97 -0.57 -1.92 67.31 57.53 2.83 Gopalganj Dist.

Raihan [28] 15.29 38.01 0.7 92.71 58.0 1.74 Sunamganj District Islam [85] 0.43 14.91 -0.49 1.55 56.48 10.92 0.17 Joypurhat District Atikul [72] 80.73 50.56 -2.83 -15.0 74 52.26 13.17 Patuakhali District Mahmud [86] 0.41 21.50 1.17 0.6 49.5 0.002 Brahmanbaria Sammi [87] 0.23 24.42 2.26 89.8 0.27 Bogra District Shirazi [10] 1.94 47.80 0.75 79.28 Trisal, M’singh Dist Sultan [27] 9.67 62.40 29.18 29.18 87.1 25.94 2.09 Khulna District Shaik [88] 0.76 36.95 -0.62 0.49 Faridpur District *According to (chronologically): Ayers and Westcot [33], Eaton [89], Todd [56], Clesceri [90], Doonen [63], Richard [60], Gupta [71], Kelley [64], Raghunath [55], Freeze [91], and Wilcox [74].

The IWQ index is an exclusive index value to assess the suitability of the irrigation water quality in the study area. Table 6 shows that the IWQ values of selected water samples of different regions of Bangladesh and Figure 6 shows three-class values (%) according to the suitability map obtained from the calculated index values. Using Equations 1 and 2 of Section 3.1, IWQindex was computed for the groundwater samples of 11 selected districts of Bangladesh. When the calculated value ranges from 22 to 37, the corresponding water exhibits medium suitability for irrigation purposes. The values of over 37 indicated that the groundwater of this region is suitable for irrigation and could be easily used for agriculture purposes. The computed IWQ index values are less than 22 demonstrate the low suitability for irrigation water. The result showed that the groundwater of the coastal belt in Bangladesh is having a high salinity hazard and the IWQindex values were found to be less than 22. It indicated that the groundwater of the coastal areas was unfit for irrigation uses. The study suggested that groundwater extraction for irrigation purposes of the areas must be considered with caution for sustainable groundwater management. The water quality of the other part of the country is almost safe for agricultural activity.

Table 6. Physico-chemical irrigational groundwater quality of Bangladesh (selected 11 District).

Sampling Area

Fulpur, M’singh Dist.

Pabna district

Physico-chemical irrigational water quality (mean value) and degree of water quality HT TDS EC Mg:Ca Na:Ca Hazard IWQ mg/L mg/L class Index μS/cm 260 192 297 0.44:1 0.24:1 C2S1 23.56 210 553 790 0.22:1 0.26:1 C1S1 23.39

Comments - No permeability problem.

- Carbonate zero but high BC, resulting high Na and SAR, and Zn deficiency in rice.

- Not suitable for irrigation.

- Good irrigation water quality in south zone.

- Problems in water uptake and infiltration.

-Serious permeability problem.

Satkhira Dist.

209

751

1430

0.36:1

2.63:1

C2S2

20.45

Comilla District

337

677

1079

1.45:1

1.79:1

C3S1

23.04

Botiaghata, Khulna Dist.

Gopalganj Dist.

576

1556

3019

0.77:1

6.38:1

C3S2

18.32

577

1639

3217

0.79:1

6.13:1

C2S2

22.21

Sunamganj District Joypurhat District Patuakhali Dist.

Brahmanbaria

3018 153 957.4 52.2

404 503 4629 233

330 733 7887 327

0.73:1 0.07:1 1.07:1 1.0:1

2.3:1 0.22:1 6.2:1 0.56:1

C2S2 C1S1 C2S3 C1S2

24.54 39.78 19.11 28.49

-Serious infiltration problem, not good for irrigation.

-Very hard but good for irrigation.

- Excellent quality for irrigation.

-serious salinity problem.

-Excellent quality for irrigation.

Bogra District Trisal, M’singh Dist.

Khulna District Faridpur District

103.6

335 -

549 -

-

-

C2S1 C1S1

41.09 34.89

- Excellent quality for irrigation - Good quality for irrigation.

532 147.65

268.78

240.6 460

1.81:1

1.40:1

C3S2 C2S1

16.63 32.32

- Not fit for irrigation.

- Good irrigation water

quality.

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Figure 4. Box plot of irrigation water quality parameters

Figure 5. The values of SAR, SSP, RSBC, and MRI in groundwater samples of the various regions of Bangladesh Table 7. The range of irrigation water quality (IWQ) index IWQindex < 22 22–37 > 37

Ratting factors 1 2 3

Suitability of water for irrigation Low Medium High

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5.

CONCLUSION To evaluate the irrigation water quality in Bangladesh (BDP), collected secondary data regarding several water quality indices (EC, salinity hazard, hardness, sodium percentage, permeability index, sodium adsorption ratio, magnesium hazard, Kelly’s ratio) from the groundwater samples of selected 11 districts. The spatial analysis of the IWQ index illustrates that higher score values for irrigation were observed in the north and north-west side of the country, whereas lower score values show in the southern coastal zones of Bangladesh. According to the score of IWQindex, it found that 25.5% of the samples (6 Districts) belong to a high suitability water class, while 41% and 33.5% exhibit medium and low suitability classes for irrigation activities in the country. The shallow-deep water of coastal areas (15% of the country area) holds excess salt and brackish water, for this reason, the water is completely unfit for irrigation. In the present study, EC, TH, TDS, SAR, SSP, MAR, RSBC, and KR values reveal that, except seaside zones, the groundwater samples belong to excellent to good quality types for irrigation uses. The hazard class of southern groundwater samples found C2S2, C3S2, or/and C2S3 categories. The study results showed a consistent index that can be used to regulate the irrigation water quality of any area. These approaches could be used to ensure the quality of groundwater consumption for agricultural purposes. Multiple water indices can be applied to prevent water deterioration, and thus, contribute to the sustainable management and policy adaptation of groundwater resources in Bangladesh.

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Design and implementation of an African native language-based programming language Ezekiel K. Olatunji1, John. B. Oladosu2, Odetunji A. Odejobi3, Stephen O. Olabiyisi4 1Department

of Computer Science, Bowen University, Iwo, Osun State, Nigeria of Computer Science and Engineering, Ogbomoso, Nigeria 3Department of Computer Science and Engineering, Obafemi Awolowo University, Ile-ife, Nigeria 2,4Department

Article Info

ABSTRACT

Article history:

Most of the existing high level programming languages have hitherto borrowed their lexical items from human languages including European and Asian languages. However, there is paucity of research information on programming languages developed with the lexicons of an African indigenous language. This research explored the design and implementation of an African indigenous language-based programming language using Yoruba as case study. Yoruba is the first language of over 30 million people in the south-west of Nigeria, Africa; and is spoken by over one hundred million people world-wide. It is hoped, as established by research studies, that making computer programming possible in one’s mother tongue will enhance computer-based problem-solving processes by indigenous learners and teachers. The alphabets and reserved words of the programming language were respectively formed from the basic Yoruba alphabets and standard Yoruba words. The lexical items and syntactic structures of the programming language were designed with appropriate regular expressions and context-free grammars, using Backus-Naur Form (BNF) notations. A prototype implementation of the programming language was carried out as a source-to-source, 5-pass compiler. QBasic within QB64 IDE was the implementation language. The results from implementation showed functional correctness and effectiveness of the developed programming language. Thus lexical items of a programming language need not be borrowed exclusively from European and Asian languages, they can and should be borrowed from most African native languages. Furthermore, the developed native language programming language can be used to introduce computer programming to indigenous pupils of primary and junior secondary schools.

Received Sep 10, 2020 Revised Jan 29, 2021 Accepted Feb 22, 2021 Keywords: BNF Lexicons Parser Programming languages Yoruba language

This is an open access article under the CC BY-SA license.

Corresponding Author: Ezekiel K. Olatunji Department of Computer Science Bowen University, Iwo Osun State, Nigeria Email: aekolatunji@gmail.com

1.

INTRODUCTION Programming languages (PLs) can be described as notational systems for communication of algorithms and data structures to computers and people. A number of factors have influenced the evolution and development of PLs. These include but not limited to discovery of weaknesses and/or deficiencies in the existing PLs; development in computer hardware; requirements of new areas of application; changing

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understanding of better methods of writing and maintaining large and complex programs; understanding of strength and weakness of some language features and the need for standardization [1], [2]. Many popular high-level languages (HLL) (such as COBOL, Pascal, Visual Basic, C++, Java and others) have been developed from the lexicons of English language while others (such as Rapira [3] and Ezhil [4] have been developed from the lexicons of Asian languages. However, there is scarcity of research information on serious efforts at designing and implementing PLs based on the lexicons of African indigenous languages, such as Yoruba language. According to [5], development of such PLs will improve computer-based problemsolving processes by indigenous teachers and learners. This fact has also been corroborated by research studies [6]-[9]. This research explored the design and implementation of an African native language-based programming language (NLPL) using Yoruba as case study. Yoruba is the first language of over 30 million people in the south-west of Nigeria, Africa; and is spoken by over one hundred million people world-wide [10].

Aside improving computer-based problem solving processes by indigenous teachers and learners, availability of NLPL will enable many millions in Africa who are only literate in their mother tongue to learn how to program the computer in their mother tongue. Over 13 million of this category of people are in Nigeria alone [2]. In addition, development and adoption of NLPL will increase the functional load of their base languages; this will consequently reduce the chances of such languages going into extinction as predicted and feared in many circles [11]-[13]. Interestingly, in a related work, in a bid to ascertain the relevance and needfulness of NLPL, Olatunji et al [14] carried out a needs assessment survey for a NLPL through design and administration of structured questionnaire. It was reported that eighty-nine percent (89%) of the respondents to the questionnaire expressed eagerness and willingness to program or learn programming in a NLPL, if one exists. The outcome of the study further gave impetus to embarking on this research.

2.

RELATED WORKS The dearth of literatures on African native language programming languages has earlier on been stated. The few available non-English-based PLs were developed primarily for pedagogical reasons; which is also the primary motivation for embarking on this research. Rapira [3] is an educational procedural programming language developed in the USSR and implemented on Agat computer, PDP-11 clones (Electronika, DVK, BK series) and Intel-8080/Z80 clones. It was developed by Andrev Petrovych Ershov, a Soviet Computer Scientist and notable pioneer in systems programming and programming language research [15]. Rapira was an interpreted language with dynamic type system and high level constructions. The language originally had a Russian-based set of keywords [3], but English and Moldovan were added later.

Rapira was used in teaching computer programming in Soviet schools.

Ezhil is an interpreted Tamil-based programming language developed by [16]. Tamil is an Indian language spoken by over 60 million people [17]. The programming language is targeted towards the K-12 (Junior high school) level Tamil speaking students as an early introduction to thinking like a computer scientist [4]. The syntax of Ezhil is broadly similar to that of conventional BASIC. According to the author of Ezhil, the primary motivation for developing the language is that “like mathematics, computing is a concept and can be introduced through any native language”. Thus by introducing computing in the native language children can easily learn how to think in the required “logical modes (enumeration, recursion, procedural)” [16]. The syntax of our programming language is similar to structured BASIC, and only Yoruba keywords are allowed.

Qalb, developed by [18], is a functional PL based on the Arabic language. This programming language enables one to write computer programs completely in the Arabic language. One of the motives for developing the programming language is to challenge the culture in which the design of most modern popular programming languages is predominantly based on the English language words. Such a culture, as noted by [19], makes learning programming especially difficult for students whose native language does not even use the Latin alphabets as does English language and for which English-based programming language keywords are little more than abstract symbols. Qalb is a programming language that deviates almost entirely from the use of ASCII character set for its encoding [18]. While Qalb’s syntax is similar to that of Lisp and Scheme, the syntax of our programming language is similar to that of structured BASIC. Furthermore, unlike Qalb, our PL made use of a mixture of ASCII and Unicode characters.

The Hindawi programming system (HPS) was described by [20] as a suite that allows users to program in Indic languages (Hindi, Bangla, Gujarati, Assamese and some other Indic languages). The HPS, developed by Chaubary A and Chaudbary S., is a free, open-source, completely non-English-based programming platform that allows non-English medium literates of India to learn and write computer programs [21]. The HPS removes the English language barrier and enables non-English literates Indians to Int J Adv Appl Sci, Vol. 10, No. 2, June 2021: 171 – 177

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take up computer science and participates in the information and communications technology (ICT) at all levels of technology from primary school education to robotics and super-computing in their mother tongue.

While their work provided a programming platform for many Indic languages, our just one African language the Yoruba language. However, the planned implementation approach for our work is similar to that of [21].

The development of a programming language called “Dolittle” was described by [22]. Its keywords are based on Japanese language. Dolitlle was developed in 2000 [23] in response to the need for an objectoriented programming language that is suitable for children in both elementary and secondary schools in Japan. It was designed to be an object-oriented educational programming language. The programming language was written in Java and does not require elaborate declarations. Unlike the work of [22], the keywords and identifiers in this research are based on Yoruba language. Furthermore, structured programming is the focus of our designed language.

3.

METHODOLOGY This research derives its theoretical underpinning from the theories of formal grammars, languages and automata. The detail design of a subset of the programming language with lexicons of Yoruba language has been carried out [5]. This was accomplished by forming the character set and reserved words of the PL from the basic Yoruba alphabets and standard Yoruba words respectively. Necessary regular expressions and regular grammar were also defined to specify the lexical structure of the language. Yoruba words (such as Sesiro, Gbawole and others) that will not lead to ambiguity are used for the design of the lexical items of the programming language in order to simplify its implementation. Furthermore, appropriate context-free grammars were defined, using Backus-Naur Form (BNF) notations and its extended version, to specify the syntactic structure of a valid program and program elements (statements, variables, expressions and so on) in the language.

A prototype implementation of the Yoruba-based PL has been carried out. Only limited constructs, including input and output (I/O) and arithmetic statements, were implemented. The Yoruba-based PL was implemented as a source – to- source compiler that produces another high – level language, QBASIC language, as output because a compiler already exists for QBASIC. This approach has been used for a number of programming languages, such as Java, Python, and others [24]. The programming language was implemented in four phases, viz: lexical analysis, syntax analysis, semantic analysis and code generation.

Recursive descent parsing algorithm was employed in implementing the syntax analysis phase. Rather than generate machine language codes, the code generation phase generated QBASIC code for constructs of the language that are syntactically and semantically valid.

Furthermore, the language was implemented as a 5-pass compiler. Each phase of the implementation formed a pass with the exception of the parser that is made up of two passes. All the components of the system were coded and test-run on the QBasic integrated development environment (IDE) using QB64 as the implementation language. QB64 is a BASIC compatible editor and C++ compiler that creates working executable files from QBasic BAS files that can be run on 32 or 64 bits PC Windows (XP, Vista and newer), Linux or Mac.

4.

RESULTS AND DISCUSSION The output of the design of a subset of the Yoruba-based PL is the syntactic definition of the PL which has been reported in [5]. Furthermore, detail sample output generated by the scanner for some given source programs in the PL has been reported in [2] and [5]. Figure 1 is a syntax error-free source program used to test the parser component of the compiler. Figure 2 and Figure 3 are the outputs generated by the parser at the end of syntax analysis of the source program. They provide information for the programmer as to the syntactic correctness or otherwise of each source statements in the source program. Figure 2 is a runtime display of the parser that gave a summary information on whether or not the source program contains syntax error, while Figure 3 provides detail status of each statements in the source program. It also provides insight into the possible causes of mistakes for statements that are in error. Examination of these outputs (Figure 2 and Figure 3) and comparing them with the input (Figure 1) show that the parser is working correctly A source program (like Figure 1) that has been parsed to be syntax error-free by the parser would be subjected to semantic checks. Though Figure 1 has no syntax error, it however, contains some semantic errors by the definition of the programming language. This is indicated in Figure 4. These errors are type incompatibility in line 4 of Figure 1 and undeclared identifier ‘Kola’ in lines 5 and 6 of the source program.

By the definition of the developed Yoruba-based PL, both the parser and semantic checker are functioning correctly. Figure 5 is another source program that has been compiled to be free of all compilation errors Design and implementation of an African native language-based … (Ezekiel K. Olatunji)

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(lexical syntax and semantics). Object code is only generated for a compilation error-free source program.

The ‘object’ code generated in QBASIC for the source program is shown in Figure 6. QBASIC code is the ‘object’ code produced because the compiler was developed as a source-to-source compiler. When Figure 6 was opened within the QBASIC 64 IDE, it was discovered to be compilation error-free also. This also establishes the functioning correctness of the code generator.

Figure 1. Yoruba source program parser

Figure 3. Output of the parser for the source program in Figure 1

Figure 2. Run-time display of the parser

Figure 4. Output of the semantic checker for the programmer (using Figure 1 as input)

Figure 5. Sample Yoruba-based source program to do arithmetic Int J Adv Appl Sci, Vol. 10, No. 2, June 2021: 171 – 177

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When Figure 6 was then run with 12 and 23 as input data, Figure 7 was produced as the run-time output. Examination of the source program of Figure 5 and the input supplied shows that the output produced (Figure 7) is correct because 12 plus 23 equals 35 and 12 multiplied by 23 equals 276.

Figure 6. Code generated for the Yoruba source program of Figure 5

Figure 7. Run-time output of the source program of Figure

5.

CONCLUSION AND FUTURE WORK Development of a programming language based on the lexicons of an African language, like Yoruba, is very much desirable and relevant, especially in Nigeria. This is attested to by the outcome of the needs survey carried out in which eighty-nine (89%) percent of respondents to the questionnaire used for needs assessment indicated their willingness to program or learn programming in their mother tongue, if one exists [14]. The successful development of the Yoruba-based programming language shows that lexical items of programming languages need not be borrowed exclusively from European and Asian languages, but can also be borrowed from most African indigenous languages. The people who are only literate in their mother Design and implementation of an African native language-based … (Ezekiel K. Olatunji)

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tongues, like Yoruba, can now be taught the art of computer programming in their native languages. In particular, computer programming, using the developed programming language, can now be introduced to primary and junior secondary school pupils instead of or in addition to using BASIC or LOGO language as is the current practice in Nigeria. For future research work, the current orthography of Yoruba language would be considered for developing a Yoruba-based PL. In this regard, some special Yoruba alphabets such as á è, é, í, ó, ù, ę, ǫ and others would be included for implementation.

ACKNOWLEDGEMENTS The authors are grateful to their families for their support and encouragement. The editors and reviewers are also gratefully acknowledged.

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E. K. Olatunji, J. B. Oladosu, O. A. Odejobi, S. O. Olabiyisi, “Towards Development of an Indigenous African Language-based Programmining Language,” FUOYE Journal of Engineering and Technology, vol. 3, no. 2, pp. 6164, 2018.

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Ezekiel Olatunji, John Babalola Oladosu, Odetunji A. Odejobi, Stephen Olatunde Olabiyisi, “A Needs Assessment for Indigenous Language-based Programming Language,” Annals of Science and Technology AST. 2019.

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M. Annamalia, “Ezhil-A Tamil programming language”, arXiv, 2009. [Online] Available: arxiv.org/pdf/0907.4960.

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BIOGRAPHIES OF AUTHORS Ezekiel K. Olatunji is the corresponding author of the article. He holds a Ph.D degree in Computer Science. He is presently a lecturer in the department of Computer Science, Bowen University, Iwo, Osun state, Nigeria.

J. B. Oladosu is an Associate Professor of Computer Engineering in the department of Computer Science and Engineering, Ladoke Akintola University of Technology, Ogbomoso, Osun State, Nigeria.

O. A. Odejobi is a full Professor of Computer Science in the department of Computer Science and Engineering, Obafemi Awolowo University, Ile-ife, Osun State, Nigeria

S. O. Olabiyisi is a full Professor of Computer Science in the department of Computer Science and Engineering Ladoke Akintola University of Technology, Ogbomoso, Osun State, Nigeria

Design and implementation of an African native language-based … (Ezekiel K. Olatunji)

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A systematic overview of secure image steganography Bakhan Tofiq Ahmed Department of Computer Science, College of Science, University of Garmian, Kalar, Sulaimani, Kurdistan Region, Iraq Department of Information Technology, Technical College of Informatics, Sulaimani Polytechnic University, Sulaimani, Kurdistan Region, Iraq

Article Info

ABSTRACT

Article history:

Information is a vital thing that needs to be secured and well protected during transmission between two or more parties over the internet. This can be achieved by steganography technology. Steganography is the concealing science in which the information is concealed inside other information in a way that the concealed information cannot be detectable by the human eye.

Many ways are available to hide data inside a cover media for example text, image, and audio steganography, but image steganography is the most utilized technique among the others. Secure image steganography has a highsecurity level than traditional technique by combining steganography with cryptography due to encrypting secret information by cryptography algorithm before embedding it into the cover media by steganography algorithm. In this paper, a systematic review has been presented about secure image steganography and its renowned types. Many researchers proposed secure image steganography by using various cryptography and steganography algorithms which have been reviewed. The least significant bit ‘LSB’ was the renowned steganography algorithm which has been used by researchers due to its simplicity, while various cryptography algorithms like advanced encryption standard (AES) and blowfish have been used to propose secure image steganography in the reviewed papers. The comparison among the reviewed papers indicated that the LSB with hash-RSA gave a greater peak signal-noise ratio ‘PSNR’ value than the others which was 74.0189 dB.

Received Jul 28, 2020 Revised Feb 28, 2021 Accepted Mar 6, 2021 Keywords: Discrete cosine transform Least significant bit Steganography Stego-image Stego-key

This is an open access article under the CC BY-SA license.

Corresponding Author: Bakhan Tofiq Ahmed Department of Information Technology Technical College of Informatics Sulaimani Polytechnic University Sulaimani, Kurdistan Region, Iraq Email: bakhan.tofiq.a@spu.edu.iq

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INTRODUCTION The fast technology development and automated life elevated the prerequisite for an additional security level. All over the globe, security is a growing requisite because a lack of security can result in great damage [1], [2]. The internet and technology are enhanced rapidly day by day. Every day a huge amount of data and information are moved to the internet so providing security for sensitive information is extremely important. Secured communication is an important issue for a long time. Two main techniques are used for providing security, namely, Cryptography and Steganography. A technique that has been created for securing the data is known as Cryptography and several various techniques have been improved to encrypt or encode and decrypt or decode data to provide safety for the information in terms of content not the existence of data that is not enough. Another technique that has been created for protecting and hiding the message's existence Journal homepage: http://ijaas.iaescore.com

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is called Steganography. It is the art, science, and technique utilized for hiding the existence of secret information. Steganography and Cryptography are two different techniques that provide security, in cryptography the contents of secret data are kept whereas in steganography the existence of secret information is kept. As a result, steganography is more secure than cryptography [3]. Steganography is a Greek word that means ‘secure writing’. A technique which is used to hide information inside information is known as Steganography which was practiced during the prehistoric time [4]. The major aim of steganography is to conceal the information inside information in an approach that is unnoticeable by the eyes of humans [5]. The information is text, image, audio, or video. Steganography has five types like text, image, audio, video, and protocol [6].

The types rely on the medium that is used as a carrier. First, a technique that is utilized to hide a secret message inside a text message is known as text steganography. It can be obtained by changing the format of the text. This type is not used often because the amount of redundant data is extremely small.

Second, image steganography means that secret information is hidden inside an image medium. In this type, a digital image is used to cover a secret message by using an algorithm with the secret key. It works with a different domain such as the Image domain, Transform domain. Third, when audio is used as a carrier then it is called audio steganography. LSB coding, Parity coding, Phase coding, Spread Spectrum, and Echo Hiding are the main audio steganography methods. Fourth, a technique which hides any file types in any video file extension is called video steganography. In other words, the video is taken as a cover in video steganography [7]. Ultimately, a technique which embeds secret information within network protocols such as TCP/IP is socalled protocol steganography. The secret message is concealed in the TCP/IP packet header. Nowadays, Image Steganography is the most widely used type. In this type, the image is utilized as a carrier to conceal the secret data. Many techniques are used in image steganography, but the most common are spatial domain, Transform domain, spread spectrum, patchwork, etc [8].

The main aim of this study is to present a comprehensive survey about a proposed secure image steganography system which is based on a combination of a cryptographic algorithm with a steganographic algorithm and compare among the relevant up-to-date research papers available in this area. The other parts of this study are structured as follows: in section 2 literature review has been presented about the most related papers in this field. Image steganography and its types have been discussed in section 3. Section 4 is about image steganography in the spatial and transform domain. Evaluation criteria were drawn in section 5 and a comparison between the reviewed papers was revealed in section 6. Ultimately, the conclusion was drawn in section 7. The categories of Steganography are shown in Figure 1.

Figure 1. Steganography categories [8]

2.

LITERATURE REVIEW Many researchers worked in this field and proposed secure image steganography to provide highlevel security by combining steganography and cryptography technology. Some of these up-to-date relevant researches are reviewed as enlisted as following: Kumar et al., [9] this study presented an embedding technique by using a hash function and Rivest Shamir Adelman ‘RSA’ algorithm for encoding data to send secret information in a trustworthy way via an unsecured channel like the Internet. Then, the encoded data has been embedded by the LSB algorithm. The proposed system’s performance has been evaluated by comparing it with the traditional LSB algorithm. The experimental outcomes have shown that the proposed system was efficient because it gave a satisfying value of both mean secure error ‘MSE’ and peak signal-noise ratio ‘PSNR’ for stego images.

Sharma et al., [10] recommended a method by joining both cryptography and steganography technology. Blowfish algorithm has taken as cryptography and LSB as steganography technique. First, the secret message is encoded by the Blowfish algorithm. After that, the encrypted secret message is hidden by A systematic overview of secure image steganography (Bakhan Tofiq Ahmed)

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the LSB algorithm. The concatenation between these two methods gives a higher level of data security. This system is measured as a very secure system because it is tough for the intruders to recover the hidden image.

Verma et al., [11] a hybrid approach is proposed for image security. First, the image is encrypted by Modified Advanced Encryption Standard (MAES) which is based on the cryptography concept to achieve better performance than the original AES. Then, the LSB algorithm is utilized to conceal the encoded image to provide secret communication. Consequently, the communication cannot be predicted by the intruder. The experimental results are shown that the proposed hybrid approach gives higher security against various attacks and a PSNR of 59.4681dB. Nag et al., [12] this paper proposed secure image steganography by mixing LSB and Huffman coding which is a cryptographic algorithm. By the proposed technique a high-security level has been obtained. Firstly, every 8 bits of the secret image is encoded by the Huffman tree. Later, the encrypted bits are split into four slices which have 0 to 3 decimal values. The experiment results showed that attackers can't extract the secret message because mixed techniques made the proposed system very secure. The proposed technique gave PSNR values were about 31 dB. Singh et al., [13] a hash-based approach with a Canny edge detection is recommended for proposing a secure color image steganography. A steganography procedure is used for encoding. First of all, various types of color (RGB) image as a cover and text data as a secret message is taken. Edge detection is carried out by the canny method and after that the text data inserted into the cover image by using a hash function.

The results are simulated by Matlab2010a. The proposed method is tested by various image type formats such as jpg, jpeg, bmp, and tiff. The results showed that the hash-based approach is a secure method to obtain secure image steganography.

Satar et al., [14] this research paper aimed to propose two security layers by merging steganography with cryptography. In the proposed system, the RSA and Diffie Hellman algorithm is examined. Encoding and decoding the secret information is done by RSA, while the Diffie Hellman algorithm allows users to embed the secret information in the selected pixel. As a result, both security and high image quality with a PSNR value of 71.9dB is achieved by the proposed system. Also, this model was more complicated and proved that secret data cannot be extracted by attackers.

Zhou et al., [15] proposed an enhanced LSB algorithm of a color image with the RSA which is mainly utilized for digital signature. In this research, the vision of the human eye and identity authentication has been incremented because it has relied on the technology of cryptography. Finally, the experiment demonstrated that the enhanced LSB is more robust than the traditional LSB method because it gave a higher security level and higher PSNR. Sharma and Srivastava, [16] a new mechanism has been implemented by combining cryptography and steganography. The advanced encryption standard (AES) algorithm has been utilized as cryptography to encode secret images before hiding them in the cover image and the 2-dimensional haar discrete wavelet transform (2-D HDWT) was applied on the cover image to extract its coefficient features. Then, alpha blending function used to mix cover image and secret image and stego image obtained after applying 2dimensional haar inverse discrete wavelet transform (2-D HIDWT) on the result of alpha blending. The proposed system gave a higher imperceptibility and trustworthiness due to the combination of steganography and cryptography.

Kusuma et al., [17] in this study, secure image steganography was proposed by using Arnold’s Cat Map (ACM) and inverted 2-bit LSB. The ACM is utilized to encode an image by the pixels’ randomization.

After award, the inverted 2-bit LSB is used to embed the ACM result into a cover. In addition, by utilizing Inverted 2-bit LSB two bits in the cover image’s bit plane were replaced with secret information bits. This replacement strategy will confuse intruders when they attempt to decode the cipher images. The experimental outcome was assessed by using PSNR and entropy to compare the stego images and the cipher images’ quality. Consequently, the proposed system gave 57.8493 dB and 7.9948 of PSNR and entropy, respectively.

Tauhid et al., [18] in this paper, a new approach was presented by combining AES with LSB to ensure a secure transmission while the information was sent between the sender and receiver. The AES is utilized to encrypt the secret info in the spatial domain of the carrier image, while LSB is used to embed secret information in the transform domain of the same image after applying a discrete cosine transform (DCT) on the pixels of the image. An extra security layer has been added to this work by performing an XOR operation on the encoded secret information with the carrier image’s pixels. The proposed system attained a high PSNR of 62.72 by this the proposed system provided three security layers of the information and errorfree decryption.

Ahmed et al., [19] in this study, two security layers were proposed by using double XOR operations using binary representation and LSB. Firstly, the message is encrypted by using a double XOR operation using binary representation, and then LSB hid the encoded data into the carrier image. To ensure the quality of their proposed system, renowned evaluation measures like MSE, PSNR, entropy, and histogram Int J Adv Appl Sci, Vol. 10, No. 2, June 2021: 178 – 187

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distribution have been calculated. The experimental outcomes showed that the proposed system preserved the security of hidden text messages and obtained a PSNR of 55.67 dB and a MSE of 0.18.

3.

AN OVERVIEW OF IMAGE STEGANOGRAPHY Image steganography is the most renowned steganography form. It means that the secret data is hidden in the image medium. In other words, when a digital image is acted as a carrier to conceal data is known as image steganography. In this form, the carrier is an image that covers secret information. The secret message can be a text message or an image that needs to be hidden inside the carrier. An image is made up of pixels. Each pixel is represented by three colors which are red, green, and blue ‘RGB’. Each color comprises 8 bits (1byte). An image can be categorized into a color, black and white, or a grayscale. A color image comprises three planes ‘RGB’ with pixel values ranging from 0-255, while a grayscale image comprises only one plane with pixel values ranging from 0-255 [20].

3.1. Image compression In images, there are two main compressions algorithms as “Lossy” Compression and “Lossless” Compression. In the “lossy” form, the amount of information is reduced before transmitting it. This reduction will be done by losing some redundant information. It means that the compressed image is not exactly like the original image. JOINT PHOTOGRAPHIC EXPERTS GROUP ‘JPEG’ is the image format that utilizes Lossy Compression. However, in “Lossless” compression the amount of information is not reduced from the target image. After the image is decompressed, all the information can be restored. However, GRAPHICAL INTERCHANGE FORMAT ‘GIF’ and BITMAP FILE ‘BMP’ are image formats that utilize Lossless Compression [21].

3.2. Image steganography terms The followings terms are used in image steganography [21]: − Cover-image: It is an image (or media) that acts as a carrier for concealing secret information. − Stego-image: The original information is embedded in the carrier image to generate a stego-image. − Message: It is original information that needs to be concealed. The information can be (plain text, ciphertext, or image). − Stego-Key: A key that plays a vital role named stego-key. It is utilized to embed and extract the secret data from the cover and the stego images.

The two main concepts used in image steganography namely, embedding and extracting process. In the embedding process, the secret message is concealed in the cover-image with help of the stego-key, so no one can extract the information without knowing the stego-key. As a result, a stego-image is attained which is ready to pass through the next process. As shown in figure 2, in the extracting process, a stego-image with the stego-key is passed through the extraction process to attain the secret information. As the stego-key is utilized in the embedding process it is also utilized in the extracting process. So the key is shared between the sender and receiver. Encoding is completed at the sender's side to attain stego-image, whereas decoding is carried out at the receiver’s side to attain secret information. Figure 2, depicts the block diagram of the Image Steganography model.

Figure 2. The image steganography’s block diagram [22] A systematic overview of secure image steganography (Bakhan Tofiq Ahmed)

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3.3. Image steganography techniques Many techniques can be used for performing Image Steganography some of them are listed as the following: Spatial or Image Domain − Least Significant Bit ‘LSB’ Transform or Frequency Domain − Discrete Cosine Transform ‘DCT’ − Discrete Wavelet Transform ‘DWT’ − Discrete Fourier Transform ‘DFT’ Spread Spectrum.

Patchwork.

Distortion Technique.

Masking and Filtering.

3.3.1. Image or spatial domain In this domain, the information is inserted directly into the original image pixels’ intensity. This technique relies on the format of the image that is utilized as a cover medium. For hiding the data in this technique some bits are directly changed into the pixel values bitwise of the image. There are many ways to perform embedding files in Spatial Domain but the easiest and simplest one is LSB [23].

3.3.2. Transform or frequency domain This steganography domain is utilized to conceal a huge data amount. It offers high security, good invisibility, and no loss of secret message. In this domain, firstly the cover image is transformed. After that, the secret message is embedded in significant areas. The transform domain can be categorized into three main kinds such as DCT, DWT, and DFT. The embedding process in this domain is more complicated than embedding data in the spatial domain because the data is not hidden directly in the pixel’s intensity, but it is concealed in the pixel’s coefficient. Furthermore, it is better than the image domain because it hides the data in a medium that is less affected by cropping and compression. JPEG image format is the common file format that is used under this domain especially with DCT [23].

3.3.3. Spread spectrum In this method, the secret data is scattered all over the cover-image so that it is tough to detect it easily by hackers. Stego-image can be produced by embedding the secret data in noise before it combines with the cover-image. As a consequence, the secret data is impossible to be visible due to that this technique is quite robust against any intruder [23].

3.3.4. Patchwork It is also known as a statistical method that utilizes redundant pattern encoding. First, the secret data is embedded by adding redundancy and then spreads out through the cover image. The intensity of a pixel might be different in each patch. If the intensity increased in one patch, it will be decreased in the other. The changes are so small that cannot be predicted by human eyes. The main limitation of this method is that solely one bit can be embedded. However, the image can be divided into sub-image, if more bits are to be embedded. In contrast, the main benefit is that if one patch is destroyed others will safe because the secret data is not hidden only in one location, but it is concealed in different locations of the image [23].

3.3.5. Distortion technique This technique is used to store the embedded info in the signal distortion. Secret messages can be restored if the original message is known during the decoding process. Knowledge and carefulness are required in this method because it is necessary to check the similarity between the original carrier-image and stego-image. The weakness of this technique is that if the cover image is used more than one time then the stego-image can be easily detected by intruders [24] 3.3.6. Masking and filtering These methods are utilized to conceal the information by marking the image which is similar to the watermarking technique. The masking and filtering technique is applied to the image with 24-bit of size or grayscale type by using different applications to hide a message. In this technique, the information imparts into a more significant image area [24].

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4. IMAGE STEGANOGRAPHY IN SPATIAL AND TRANSFORM DOMAIN 4.1. Image steganography in the spatial domain It is also referred to as the Image domain. It applies a bit insertion between secret information and a carrier image. In this domain, the secret data is directly inserted into the actual image pixel’s intensity value.

The pixels value is either 8-bit, 16-bit or 24-bit relied on the standard of the image. The easiest and simplest method under this technique is the LSB method. The secret information is converted into a series of bits before embedding secret information into a cover image [25].

4.1.1. Least significant bit ‘LSB’ LSB is the easiest and simplest algorithm. The cover image’s least significant bit (8-bit) is altered by the bit of the hidden message. It is utilized to insert hidden data in a cover image sometimes it is referred to as LSB Replacement. Because the LSB method depends on changing the redundant bits that are less important or significant with the secret information bits, particularly the rightmost bits will be replaced with the bits of the secret data because it does not affect the image’s quality. The aim of LSB is to transmit the secret data to the receiver without knowing to the attacker that the information is being transmitted. Although LSB is an easy and quick method, it has a weakness, which can be easily detected by an attacker [25].

4.1.2. LSB in bitmap file (BMP) In this technique, a 24-bit BMP image format is used which consists of RGB color. Each bit of the red, green, and blue ‘RGB’ colors are changed with the bit of secret information since each color is denoted by a single byte (8-bit). In other words, a 24-bit BMP image format can store 3 pixels. BMP file format uses a lossless compression technique. LSB in BMP images can hide a large amount of information. This is counted as a disadvantage because a large number of bits need to be altered. As a result, it can be easily detectable by the human eye [25]. There is an example for LSB, 3 pixels grid of a 24-bit image can be shown as: (00100001 00010100 11010101) (10110111 11010101 00101101) (11011010 10100101 01101011) 199 taken as an example, a binary representation of this number is that 11000111, is embedded into the least significant bits of this part of the image. The resulting grid is as: (00100001 00010101 11010100) (10110110 11010100 00101101) (11011011 10100101 01101011) The above number was embedded in the grid. The last bit of each RGB color is altered with the bits of the number. As a result, the last bit is altered in each pixel which is the least significant bits. Consequently, these small changes are invisible to human eyes.

4.1.3. LSB in a graphical interchange format (GIF) It is also referred to as Palette Based LSB. In this technique, a GIF image format is used as a cover image. GIF Image has a depth of 8-bit, but can be described by 256 different colors in the palette, since each color has an index which kept in a look-up table. GIF is an image format using a lossless compression technique. In the lossless compression method, the original image’s quality is well protected. It means that the compressed image and the actual image are the same. Furthermore, this form has relied on the format of the file and the image and it can hide a large message. The secret message could be visible if a cover image is selected incorrectly. The problem with this approach is that if one change in LSB‘s pixel occurs, it can result in a completely altered color because the color index is altered. This problem can be tackled by utilizing GrayScale images. In an 8-bit GrayScale GIF image, there are 256 gray shades. The colors are gradually changed in the GrayScale GIF image so it is hard to detect these changes [26].

4.2. Image steganography in the transform domain It is also referred to as the Frequency domain. The transform domain technique aims to conceal a large amount of information in the image which is less visible for cropping, compression, and image processing. By this, high security will be provided and the secret message cannot be noticed by the eyes of the human. Also, the transform domain technique is more robust concerning common image processing operations and lossy compression. There are various methods under this domain that is used for A systematic overview of secure image steganography (Bakhan Tofiq Ahmed)

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Steganography like DCT, DWT, and DFT, whereas the most common is DCT. The most utilized image file format that works with this domain is JPEG [27].

4.1.2. Discrete cosine transform ‘DCT’ This form is utilized in the JPEG image. JPEG uses a lossy compression technique. One advantage of JPEG compression is that the size of the file can be reduced by decreasing the color information [28]. In the DCT technique, the actual image is first converted from the image domain into the transform domain.

Next, the alteration is carried out by sorting the pixels into n×n blocks, and then DCT is applied on each block. A mathematical calculation is used to change the pixels and then the position of the pixel values is scattered over the image part. Later, the transformed image is divided into three frequency components (low, high, and middle). A large feature of pixels is located in the low-order DCT coefficients, whereas a fine feature of pixels is located in the high-order. As a result, the secret information is embedded in the selected high-order coefficients. The process of embedding is applied by just altering the images’ coefficients [29].

4.1.3. Discrete wavelet transform ‘DWT’ It provides a powerful algorithm for processing the image and accomplishing steganography with DWT became more popular in the information hiding era due to its simplicity. The embedding process is carried out in DWT by modifying the cover-image’s wavelet coefficients to attain a secure transmission. The component frequency band is split into four smaller bands called sub-bands namely low low ‘LL’, low high ‘LH’, high low ‘HL’, and high high ‘HH’ [30, 31]. The major advantage of DWT is that it provides high robustness due to transforming the actual image into its wavelet coefficient [32].

4.1.4. Discrete fourier transform (DFT) It is the transform of a finite and discrete-time function. The DFT computes the Bk from xn. The DFT is computed based on (1): Bk = 1 N ∑ xn N − 1 n = 0 e − 2πikn N (6)K = 1,2, … N − 1

(1)

Where the Bk is the amplitude and phase of the various components of the input signal xn [33]

5.

EVALUATION CRITERIA Each steganography algorithm has some strong and weak points, for evaluating these; a steganography method has to meet some basic requirements. The most critical requirement is that the results have to be unnoticeable and undetectable by human eyes.

5.1. Invisibility The first and most critical requirement of a stenographic algorithm is imperceptibility because the stenography’s strength is based on its ability to be unseen by the human eye [34].

5.2. Payload capacity It means that how much data can it hide? The main goal of steganography is to conceal secret data as watermarking that embeds only a small amount of copyright information [34].

5.3. Robustness against statistical attacks Statistical Steganalysis is the observation practice to detect concealed information by performing some statistical tests on image data. Several steganography algorithms leave a “sign” during the embedding process. Thus, these signs can be easily noted by statistical analysis [34].

5.4. Robustness against image manipulation The image might be altered by an active attacker to obtain the hidden information, while the image is being transmitted via a communication channel. In addition, some image manipulation, for instance, cropping or rotating can be applied to the image before it reaches its target [34].

5.5. Independent of file format There are several types of file formats on the Internet, so using only the same image file format simultaneously between the sender and receiver might be doubted. The most powerful steganography algorithms are that which can hide information in any image file format.

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6.

RESULTS AND DISCUSSION Image steganography is a critical technique for providing secure communication while transmitting information via an unsecured line like the internet. On the other hand, secure image steganography is more securable than the classical method because the secret information encrypts by cryptography technique before concealing it by steganography technique, so two levels of security are done in secure image steganography. In this study, the most relevant and up-to-date research papers that proposed secure image steganography have been reviewed. As a result, a comparison has been done among the reviewed papers in terms of used steganography and cryptography algorithms, image database, PSNR, advantages, and limitations as tabulated in Table 1.

Table 1. The comparison among reviewed papers Ref.

Year published

Steganography algorithm used

[9]

2013

LSB

Cryptography algorithm used Hash- RSA

73.5444 74.0189 73.8220 73.8528

Image database used Barbara Lena Tulips Baboon

[10]

2013

LSB

Blowfish

-

Baboon

[11]

2013

LSB

Modified AES (MAES)

2014

LSB

Huffman coding

[13]

2015

Canny edge detection

Hash function

[14]

2016

Diffie Hellman

RSA

[15]

2016

Improved LSB-Insertion

RSA-Digital signature

59.4681 30.48 30.28 30.91 30.36 39.6310 38.6527 41.5895 71.8 71.9 71.9 56.513

Flower House Peppers Lena Baboon Airplane Boat Lena Peppers Baboon Lena Peppers Baboon Lena

[12]

[16]

2017

2-D HDWT, alpha blending, 2-D HIDWT

AES

58.7501 45.8089 47.9688

Man Pepper Flower

[17]

2018

Inverted 2-bit LSB

57.8493 -

Lena Baboon Airplane Boat

[18]

2019

LSB

Arnold’s transformation or Arnold’s Cat Map (ACM), ACM with RSA AES

62.89 62.72 66.15 62.88

Lena Baboon Cameraman Zelda

[19]

2020

LSB

double XOR operations using binary representation

40.74 49.23 55.67

Lena Barbara Man

PSNR (dB)

Advantages

Limitations

Practical and reliable for sending data, a good MSE and PSNR achieved for stego-image.

Robustness, it is very difficult for an intruder to recover the secret message.

Securable against intruders.

Secure and gave acceptable PSNR.

The proposed method was tested by using only one image format.

More credible due to using a hash function.

Very secure.

More complicated.

More robust than the traditional LSB.

Implementation is hard due to the complexity of the algorithm.

Providing a high level of security for both encryption and decryption.

Higher capacity and PSNR value.

Implementation is complex.

3 security layers of the information and error-free decryption.

2 layers of security: encryption and hiding.

-

Secret messages cannot be easily deciphered if the image format is a lossy compression.

-

-

More complex.

-

-

7.

CONCLUSION Nowadays, a huge amount of data moves and transmits via the internet, so providing security for data is critical and vital. This protection can be obtained via a secure image steganography technology combined with cryptography. Cryptography aims to hide the information so no one can know about the information except the sender and receiver. On the other hand, Steganography is the technique for hiding the A systematic overview of secure image steganography (Bakhan Tofiq Ahmed)

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existence of the information, so it is difficult to detect by human eyes. In this study, a systematic and comprehensive review has been done about secure image steganography. In the literature review, various upto-date research papers had been reviewed that proposed secure image steganography by combining steganography and cryptography methods to provide a high-security level. Most of the proposed work used LSB for steganography due to its simplicity, while for cryptography various algorithms have been used such as AES, MAES, RSA, and Blowfish. Moreover, in this paper, an overview of steganography types such as text, image, audio, video, and protocol along with its renowned techniques have been presented. A comparison between the spatial domain and transform domain with their various types such as LSB, DCT, DFT, and DWT has been studied. LSB is simpler and less secure than DCT. The required criteria for evaluating steganography techniques are also explained. As a result, a comparison between the reviewed papers that combined both steganography and cryptography algorithms have been done as depicted in table 1.

The comparison indicated that the LSB with Hash-RSA attained a higher PSNR value than the other which was 74.0189 dB. It can be concluded that both steganography and cryptography are methods utilized for protecting information but when they are combined a higher level of security can be achieved because the information is first encrypted by cryptography and then concealed by steganography, so it is extremely tough for an intruder to attain the secret data.

For future study, I intend to propose a secure image steganography model by using a combination of a new cryptography algorithm like elliptic curve cryptography (ECC) and a steganography algorithm like pixel value difference (PVD).

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BIOGRAPHY OF AUTHOR Bakhan Tofiq Ahmed received the B.Sc. in Software Engineering at Salahaddin UniversityErbil- Kurdistan Region- Iraq, in 2010. She obtained the M.Sc. in IT at Sulaimani Polytechnic University- Sulaimani- Kurdistan Region- Iraq, in 2020. Her research interests are in information security, image processing, artificial intelligence, swarm intelligence algorithm, and Biometric system design. She published 5 research articles, 4 articles published in a reputed international journal, and 1 article in a national journal

A systematic overview of secure image steganography (Bakhan Tofiq Ahmed)

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Application of PSO for optimal coordination of directional overcurrent relays in distribution system with distributed renewable energy sources Lazhar Bougouffa1, Abdelaziz Chaghi2 1Department

of Electrical of Engineering, Faculty of Technology, University of El-Oued, El-Oued, Algeria Research Laboratory, Department of Electrical of Engineering, Faculty of Technology University of Batna 2, Batna, Algeria

2LSP-IE

Article Info

ABSTRACT

Article history:

The use of Distributed Renewable Energy Sources in the electrical network has expanded greatly. But, integration of these resources into distribution systems caused more problems in protection related issues such as miscoordination, and changes the direction and value of fault currents. When connecting new D-RES to electrical power distribution networks, it is required to re-coordinate Directional Over-Current Relays (DOC-Relays) to ensure the continuity of the power transmission when the short circuits take place. This work presented a Particle Swarm Optimization (PSO) algorithm to determine two independent variables called Pickup current (Ip) and Time Dial Setting (TDS) for optimal setting of relays. From analysis result, the impacts of RES location in the distribution system on DOCRs had been observed on the optimal relays settings.

Received Aug 13, 2020 Revised Feb 12, 2021 Accepted Feb 22, 2021 Keywords: Distributed renewable energy sources DOCRs Power system protection PSO

This is an open access article under the CC BY-SA license.

Corresponding Author: Lazhar Bougouffa, Department of Electrical of Engineering University of El-Oued PO BOX 789, 39000, El-Oued, Algeria Email: bougouffa-lazhar@univ-eloued.dz

1.

INTRODUCTION Distributed renewable energy generation is small power-generating unit clubbed with modern technologies and present diverse challenges while integrating with utility grid Most of the distributed renewable energy sources (D-RESs) shall be located near load centre on distribution grid. D-RES introduces negative effects on system operation. One of the negative impacts is relay coordination [1]. The integration of distributed renewable energy sources (D-RES) on the electrical network contains many advantages.

However, the result of introducing these energies in the network will change the value and direction of energy flow as well as short-circuit current levels in different points .Several factors may lead to the effects of RES energies on protection devices, including the type of technology, capacitance and the position in the network [2].

The authors in [3], proposed a dual simplex method to find the setting of TDS while keeping constant values of Ip in modified IEEE 33-bus with installing the D-RES. In the present article, a Particle swarm optimization is proposed to find out the new setting for both TDS and I P of relays with respect to various constraints in the presence of two D-RES.

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2.

DIRECTIONAL OVER-CURRENT RELAYS For optimal coordination of DOC Relays, it is necessary to determine the optimal values of TDS and IP of each relay in the system, this optimization of TDS and IP for minimize the operating time of the primary relays. The tripping time equation of DOC Relay is a non-linear equation, Depending on the fault current and both TDS and IP settings. Thus, the relay tripping time equation for DOC Relay is given by (1) [4], [5].

0,14

𝑇𝑜𝑡 = 𝑇𝐷𝑆 × (

𝐼𝑓 𝐾𝐶𝑇×𝐼𝑝

(1)

0.02

)

−1

Where, KCT is the current transformer ratio.

The pickup value is the minimum value of the current for which the relay operates. The operating time (T ot) of the relay is defined by the TDS for each current value. The limits on the TDS can be presented as (2) 𝑇𝐷𝑆𝑖𝑚𝑖𝑛 ≤ 𝑇𝐷𝑆𝑖 ≤ 𝑇𝐷𝑆𝑖𝑚𝑎𝑥

(2)

The TDS are assumed to vary between 0.05 and 1.2. 𝑚𝑖𝑛 𝑚𝑎𝑥 𝐼𝑃𝑖 ≤ 𝐼𝑃𝑖 ≤ 𝐼𝑃𝑖

(3)

The pickup current setting Ip are assumed to vary between 0.25 and 2.5 with step 0.25 When a fault occurs, there must be primary protection for isolat as soon as possible to reduce the isolated area as much as possible, and in the case of primary relay, other relay should be protected as backup protection to assure the requirement of selectivity. In order to satisfy selective requirements, you must add the following limitation [6], [7]. 𝐹𝐼 𝐹𝐼 𝑇𝑏𝑎𝑐𝑘−𝑢𝑝 − 𝑇𝑝𝑟𝑖𝑚𝑎𝑟𝑦 ≤ 𝐶𝑇𝐼

(4)

𝑇𝑗𝐹𝐼 − 𝑇𝑖𝐹𝐼 ≤ 𝐶𝑇𝐼

(5)

Where TjF1 is the tripping time of jth backup relay; TiF1 is the tripping times of ith primary relay.

The CTI is the minimum time gap in operation between the primary and its backup relay, is usually selected between 0.2 s and 0.5 s [4], [7], [8]. The CTI is set to a desired value of 0.3 sec.

3.

IMPLEMENTATION OF PROPOSED PSO ALGORITHM ON THE COORDINATION PROBLEM The Particle Swarm Optimization (PSO), which has gained rapid popularity as an efficient optimization technique, is relatively a recent heuristic introduced by Eberhart and Kennedy [9]. The various steps involved in the implementation of PSO to the DOCRs problem with 64 decisions variables are: Step1. Input the data of 33 IEEE distribution test system for calculate the power flow and current Step2. Define population size (50), no of iteration (=500), assume suitable values of PSO parameters Step3. Initial searching points and velocities are randomly generated within their limits. Pbest is set to each initial searching point. The best-evaluated values among individual best (Pbest ) are set to global best (gbest).

Step4. New velocities are calculated using the equation (9).

Step5. Evaluate the fitness values for new searching point. If evaluated values of each agent is better than previous Pbest then set to Pbest. If the best Pbest is better than best gbest then set to gbest.

Step6. If the maximum iteration is reached stop the process otherwise go to step3.

The summation of tripping times of all primary relays is known as objective function (OF).

Conventionally, the optimal coordination problem determines two parameters, that is, the pickup current setting IP and the time dial setting TDS. The OF is given by: 𝑂𝐹 = 𝑚𝑖𝑛 ∑𝑁 𝑖=1 𝑡𝑖𝑙

(6)

Where: OF is the objective function in sec, Application of PSO for optimal coordination of directional over-current Relays…, (Lazhar Bougouffa)

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til is the operating time of the ith relay, N is the total DOCRs in the system.

The two variables in the objective function are TDS and Ip. By minimizing both the TDS and Ip we can able to minimize the tripping time of the primary relays and satisfying the CTI. 3.1. Goal of Study This work, presented the PSO algorithm to find the optimal CTI of DOC Relays. The proposed algorithm was evaluated using IEEE 33-bus system in presence of two D-RESs. The main contributions of this paper are using the optimization technique to find optimal relay settings, solve the non-linear coordination problem of DOC Relays with the system changed topology.

4.

CASE STUDIES In this paper IEEE 33-bus radial distribution feeder is considered to optimal pair of DOC Relays in presence of two emplacements of D-RES. The operating voltage is 12.66 kV. DOC Relays are used in the system to protect the feeder in case of three phase faults. The IEEE 33-bus system is presented in Figure 1 [10], [11]. The model is simulated in MATLAB software without and with Renewable Energy Sources to calculate the optimal setting of DOCRs using PSO method under system changes. The program is implemented for two emplacements of Renewable Energy Sources. Three phase Faults are generated on each bus.

Figure 1. Power distribution system of the IEEE 33-bus system under study

4.1. Impact of the D-RES on the short circuit level From a power perspective, the integration of a new D-RES into the distribution networks will increase the power of the network. Thus the new source will be modeled in such a way as to take only its current contribution in the event of a short circuit. The electrical network, of which we will determine the different short circuit currents without (and with) D-RES, has a radial architecture Figure 1, and we take a part of this network for the calculations of short circuit currents, as show in Figure 2.

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Figure. 2. Simple distribution network with RES The current in the fault point will be the sum of the short circuit current without D-RES and the short circuit current injected into the network only by the D-RES, is given by (7) 𝐼𝑐𝑐 = 𝐼 𝑔𝑟𝑖𝑑 𝑐𝑐 + 𝐼 𝐷−𝑅𝐸𝑆 𝑐𝑐

(7)

The direct impedance seen between the bar (11) and the earth is (8) 𝐷−𝑅𝐸𝑆 𝑧 𝐷−𝑅𝐸𝑆 𝑑 = 𝑧 𝐷−𝑅𝐸𝑆 𝑑−𝑐𝑐 + 𝑗𝑋𝑐𝑐 + 𝑍𝑑−𝐿𝑖𝑛𝑒2

(8)

Implies that (9), (10), (11). 𝐼𝑎𝐷−𝑅𝐸𝑆 =

𝑝

𝑉𝑑

(9)

𝐷−𝑅𝐸𝑆 +𝑍 𝑍 𝐷−𝑅𝐸𝑆 𝑑−𝑐𝑐 +𝑗𝑋𝑐𝑐 𝑑−𝐿𝑖𝑛𝑒2

𝐼𝑏𝐷−𝑅𝐸𝑆 = 𝑎2 . 𝐼𝑐𝐷−𝑅𝐸𝑆 = 𝑎.

𝑝

𝑉𝑑 𝑍 𝐷−𝑅𝐸𝑆

(10)

𝐷−𝑅𝐸𝑆 +𝑍 𝑑−𝑐𝑐 +𝑗𝑋𝑐𝑐 𝑑−𝐿𝑖𝑛𝑒2 𝑝

𝑉𝑑 𝑍 𝐷−𝑅𝐸𝑆

(11)

𝐷−𝑅𝐸𝑆 +𝑍 𝑑−𝑐𝑐 +𝑗𝑋𝑐𝑐 𝑑−𝐿𝑖𝑛𝑒2

We find the fault current is (12), (13), and (14). 𝐼𝑎 =

𝑝

𝑉𝑑𝑃 𝑍𝑑−𝑐𝑐 +𝑍𝑑−𝐿𝑖𝑛𝑒1 +𝑍𝑑−𝐿𝑖𝑛𝑒2

𝐼𝑎 = 𝑎2 . [ 𝐼𝑐 = 𝑎. [

+

𝑉𝑑 𝑍 𝐷−𝑅𝐸𝑆

𝑝

𝑉𝑑𝑃 𝑍𝑑−𝑐𝑐 +𝑍𝑑−𝐿𝑖𝑛𝑒1 +𝑍𝑑−𝐿𝑖𝑛𝑒2 𝑉𝑑𝑃

𝑍𝑑−𝑐𝑐 +𝑍𝑑−𝐿𝑖𝑛𝑒1 +𝑍𝑑−𝐿𝑖𝑛𝑒2

(12)

𝐷−𝑅𝐸𝑆 +𝑍 𝑑−𝑐𝑐 +𝑗𝑋𝑐𝑐 𝑑−𝐿𝑖𝑛𝑒2

+

𝑉𝑑

𝐷−𝑅𝐸𝑆 +𝑍 𝑍 𝐷−𝑅𝐸𝑆 𝑑−𝑐𝑐 +𝑗𝑋𝑐𝑐 𝑑−𝐿𝑖𝑛𝑒2

]

(13)

𝑝

+

𝑉𝑑

𝐷−𝑅𝐸𝑆 +𝑍 𝑍 𝐷−𝑅𝐸𝑆 𝑑−𝑐𝑐 +𝑗𝑋𝑐𝑐 𝑑−𝐿𝑖𝑛𝑒2

]

(14)

5.

RESULTS AND DISCUSSION Two locations are chosen for installing the D-RES in the distribution system; to illustrate the effects of D-RES insertions on the setting of Relays. A minimum relay tripping time is the main goal of setting of relays. Also the CTI is satisfied (i.e., CTI ≥ 0.3). Table 1 shows the optimal results of TDSs in presence of DRES installation in the 33-bus distribution system. Table 2 shows the optimal results of Ips in presence of DRES. Table 1. Setting values of relais TDS Relays TDS1 TDS 2 TDS 3 TDS 4 TDS 5 TDS 6 TDS 7 TDS 8 TDS 9 TDS 10 TDS 11 TDS 12 TDS 13

Setting of TDS Without D-RES With D-RES 0.5000 0.5000 0.3500 0.3500 0.3400 0.3400 0.3300 0.3300 0.3400 0.3000 0.3500 0.3500 0.2700 0.2700 0.2400 0.2000 0.3100 0.3800 0.4600 0.5700 0.4200 0.5200 0.3000 0.4000 0.3400 0.4500

Table 2. Setting values of relais Ip Relays Ip1 Ip 2 Ip 3 Ip 4 Ip 5 Ip 6 Ip 7 Ip 8 Ip 9 Ip 10 Ip 11 Ip 12 Ip 13

Setting of Ip Without D-RES With D-RES 0.7300 0.7300 0.7500 0.7500 1.0400 1.0400 0.8100 0.8100 0.3500 0.5000 0.3500 0.3500 1.0700 1.0700 1.0100 1.2000 0.3600 0.3600 0.5200 0.5200 0.5600 0.5300 0.5400 0.5100 0.5600 0.5500

Application of PSO for optimal coordination of directional over-current Relays…, (Lazhar Bougouffa)

192



ISSN: 2252-8814

Table 1. Setting values of relais TDS (Continued) Relays TDS 14 TDS 15 TDS 16 TDS 17 TDS 18 TDS 19 TDS 20 TDS 21 TDS 22 TDS 23 TDS 24 TDS 25 TDS 26 TDS 27 TDS 28 TDS 29 TDS 30 TDS 31 TDS 32

Setting of TDS Without D-RES 0.3700 0.3600 0.3000 0.3200 0.4000 0.2600 0.3500 0.3200 0.3300 0.2900 0.2800 0.4300 0.4400 0.3200 0.3300 0.3400 0.2600 0.3300 0.4200

With D-RES 0.4100 0.4500 0.3900 0.4500 0.0700 0.1700 0.3700 0.3300 0.0900 0.0500 0.3200 0.4000 0.3800 0.2600 0.2700 0.3700 0.2800 0.3500 0.4400

Table 2. Setting values of relais Ip (Continued) Relays Ip 14 Ip 15 Ip 16 Ip 17 Ip 18 Ip 19 Ip 20 Ip 21 Ip 22 Ip 23 Ip 24 Ip 25 Ip 26 Ip 27 Ip 28 Ip 29 Ip 30 Ip 31 Ip 32

Setting of Ip Without D-RES 0.5200 0.5300 0.5000 0.8300 1.2200 1.0300 0.5000 0.5500 0.9800 1.0200 1.0100 0.5200 0.5500 0.5700 0.5200 0.7200 1.5600 1.0900 0.5100

With D-RES 1.0500 0.5000 0.5300 0.5300 1.2300 1.0000 0.5200 0.5100 1.0300 1.0200 0.9800 0.7500 0.5200 0.5100 0.5600 0.7400 1.6000 1.1300 0.5200

The results obtained after the study from the proposed PSO Algorithm of the impact of D-RES on the DOC-Relays settings are displayed in Tables 1 and 2. By examining the results obtained, it can be said that D-RES increased the values of short circuit currents at the fault point. This increase will be reflected in the reduced operating time for protection before damage to the equipment that makes up the electrical network.

6.

CONCLUSION In this paper the authors presented the Particle Swarm Optimization method to explain and visualize the influence of D-RES on the protection settings of DOC Relays in the test system. The result of using PSO algorithm on an IEEE 33-bus is compared in two cases with and without D-RES. From analysis result, the impacts of D-RES location in the distribution system had been observed on the optimal relays settings. The results show the optimal settings of DOC-relays for eliminate the three fault currents.

REFERENCES A. Shrivastava, D. Kumar Saini, M. Pandit, “Relay co-ordination optimization for integrated solar photo-voltaic power distribution grid,” Cogent Engineering, vol. 6, no. 1, pp. 1-19, 2019.

[2] R. M. Chabanloo, H. A. Abyaneh, A. Agheli, H. Rastegar, “Overcurrent relays coordination considering transient behaviour of fault current limiter and distributed generation in distribution power network,” IET Generation, Transmission & Distribution, vol. 5, no. 9, pp. 903-911, 2011.

[3] L. Bougouffa, A. Chaghi, “Effect of renewable energy sources integration on the optimal coordination of directional over-current relays in distribution system,” International Journal of Applied Power Engineering IJAPE, vol. 9, no. 3, pp. 250-255, 2020.

[4] P. M. Anderson, “Power System Protection,” McGraw-Hill, New York. 1999.

[5] A. S. Noghabi, H. R. Mashhadi, J. Sadeh, “Optimal Coordination of Directional Over-current Relays Considering Different Network Topologies using Interval Linear Programming,” IEEE Transactions on Power Delivery, vol.

25. pp. 1348-1354. 2010.

[6] Quanming Yue, Feipeng Lu, Weiyong Yu, Jie Wang, “A novel algorithm to determine minimum break point set for optimum cooperation of directional protection relays in multiloop networks,” in IEEE Transactions on Power Delivery, vol. 21, no. 3, pp. 1114-1119, July 2006.

[7] T. Amraee, “Coordination of Directional Overcurrent Relays Using Seeker Algorithm,” in IEEE Transactions on Power Delivery, vol. 27, no. 3, pp. 1415-1422, July 2012.

[8] Panigrahi B. K, Manohar Singh, A.R. Abhyankar, “Optimal coordination of directional over-current relays using Teaching Learning-Based Optimization (TLBO) algorithm,” International Journal of Electrical Power and Energy Systems, vol. 50, pp. 33-41, 2013.

[9] R. Eberhart, J. Kennedy, “Particle Swarm Optimization,” in Proceedings of IEEE International Conference on Neural Networks,” vol. 4, 1995, pp. 1942-1948.

[10] L. Bougouffa, A. Chaghi, “Optimal Coordination of DOCR for Radial Distribution Systems in Presence of TCSC,” International Journal of Power Electronics and Drive System, vol. 7, no. 2, pp. 311-321, 2016.

[11] L. Bougouffa, A. Chaghi, “Dual Simplex Method for Optimal Coordination of DOCR’s in Distribution System with D-FACTS,” International Journal of Information Science & Technology, vol. 3, no.3, pp. 3-9. 2019.

[1]

Int J Adv Appl Sci, Vol. 10, No. 2, June 2021: 188 – 192

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