
JOURNAL OF
Journal of Engineering Science and Technology Review 4 (1) (2013) 68-73

Engineering Science and
Technology Review
www.jestr.org
Research Article
Phased Array Synthesis Using Modified Particle Swarm Optimization
M. A. Zaman *, Md. M. Alam, and Md. Abdul Matin.
Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka – 1000, Bangladesh.
Received 2 September 2010; Revised 4 October 2010; Accepted 25 January 2011
___________________________________________________________________________________________
Abstract
In this paper, a linear phased array is synthesized to produce a desired far field radiation pattern with a constraint on
sidelobe level and beamwidth. The amplitude of the excitation current of each individual array element is optimized to
give desired sidelobe level and beamwidth. A modified particle swarm optimization (PSO) algorithm with a novel
inertial weight variation function and modified stochastic variables is used here. The performance of the modified PSO is
compared with standard PSO in terms of amount of iterations required to get desired fitness value and convergence rate.
Using optimized excitation amplitudes, the far field radiation pattern of the phased array is analyzed to verify whether
the design criterions are satisfied.
Keywords: Antenna array, particle swarm optimization, phased array.
__________________________________________________________________________________________
1. Introduction
Where FF is the blah blah.
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2. Formulae
2.1. Formula for the blah
The formula blah is blah and blah:
FF ( ,  )  EP( )  AF ( ,  )
0 dB,
 47 dB,
FFdesired ( )  
(1)
 4.5    4.5
otherwise
______________
* E-mail address: [email protected]
ISSN: 1791-2377  2011 Kavala Institute of Technology. All rights reserved.
1
M. A. Zaman, Md. M. Alam, and Md. Abdul Matin/Journal of Engineering Science and Technology Review 4 (1) (2011) 63-67
2.2. Other Formula
As equations (11)-(14) are coupled non-linear system of
equations, subject to the boundary conditions (15) an
analytical solution is not possible. So, we now solve it by
finite difference technique. The Crank-Nicolson scheme is
applied and there equations reduce to following form,
ruij11  2(r  1)uij 1  ruij11  Aij
Power Station
Availability
Factor
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
KAINJI
JEBBA HYDRO
SHIRORO
EGBIN STEAM
TRANS-AMADI
A.E.S
SAPELE
OKPAI GAS
AFAM (I-V)
AFAM VI
DELTA GAS
GEREGU GAS
OMOKU GAS
OMOTOSHO
IBOM
OLORUNSHOGO
0.586
0.792
0.674
0.743
0.256
0.783
0.195
0.929
0.068
0.649
0.289
0.725
0.961
0.890
0.078
0.943
Average
Availability
(MW)
445.45
457.99
404.56
980.89
25.60
236.44
199.07
446.25
63.52
322.82
255.33
300.00
96.05
298.15
2.90
315.75
BUSES
Shiroro
S/NO
21
2
3
4
Afam
Ikot-Ekpene
PortHarcourt
Aiyede
Ikeja west
Papalanto
Aja
Egbin PS
Ajaokuta
Benin
Geregu
Lokoja
Akangba
Sapele
Aladja
Delta PS
Alaoji
Aliade
New Haven
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
(17)
3. Tables
S/N
S/NO
1
Installed Capacity(MW)
760
578.40
600.00
1320.00
100
302.00
1020.00
480.00
931.60
497.25
882.00
414.00
100.00
335.00
37.00
335.00
S/NO
41
BUSES
Yola
22
23
24
BUSES
New Haven
South
Makurdi
B-kebbi
Kainji
42
43
44
Gwagwalada
Sakete
Ikot-Abasi
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Oshogbo
Onitsha
Benin North
Omotosho
Eyaen
Calabar
Alagbon
Damaturu
Gombe
Maiduguri
Egbema
Omoku
Owerri
Erunkan
Ganmo
Jos
45
46
47
48
49
50
51
52
Jalingo
Kaduna
Jebba GS
Kano
Katampe
Okpai
Jebba
AES
Tab. 2. Blah Blah Table
Tab. 1. Blah table
4. Figures
Fig. 1.Α. Profiles of velocity component u
Fig. 1.Β. Profiles of velocity compent u
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5. Bullets
Εάν το κείμενο περιέχει bullets:
 Πρώτο
 Δεύτερο
 Τρίτο
 Τέταρτο
Εάν είναι γραμμένο έτσι, πάλι δεν μας πειράζει:
 Πρώτο: Κάτι
 Δεύτερο: Κάτι άλλο
 Τρίτο: Ακόμα κάτι
2
M. A. Zaman, Md. M. Alam, and Md. Abdul Matin/Journal of Engineering Science and Technology Review 4 (1) (2011) 63-67
______________________________
References
1. Omorogiuwa Eseosa, “Efficiency Improvement of the Nigeria
330KV network using FACTS Device, University of Benin,
Benin City 2011.
2. F.D Galiana, K Almeida, “Assessment and control of the Impact
of FACTS devices on power system performance”, IEEE
Transactions on power systems, Vol .II, No 4, pp1931- 1936,
November 1996.
3. E.Acha, C.R Fuerte-Esquirel, H .Ambriz-perez and C. AngelesCamacho, FACTS: Modelling and Simulation in power
networks. Chictiester, U.K. Wiley, 2004.
4. V.K Sood, HVDC and FACTS Controllers Applications of static
converters in power systems. Boston, M.A. Kluver Academic
Publisher, 2004.
5. P. Moore and P.Ashmole, “flexible AC Transmission system,
“Power Engineering Journal, Vol. 9, No.6, pp 282-286, Dec,
1995.
6. D.J. Gothan and G.T. Heydt, “Power flow control and power
flow studies for system with FACTS Devices”, IEEE Trans
power system, Vol 13. No 1, February 1998.
7. K. Vijayakvmar, R.P Kumudinideri, “A new method for optimal
location of FACTS Controllers Using Genetic algorithm”,
Journal of theoretical and applied information technology, 2005
– 2007 Jatit.
8. S.Gerbex, R. Cherkaoui and A.J. Germond. “Optimal location of
multiple type FACTS Devices in a power system by means of
Genetic algorithm. “IEEE Trans power systems. Vol. 16, pp.
537-544, August 2001.
9. T.T. Lie and W.Deng, ”Optimal flexible AC Transmission
systems (FACTS) Devices Allocation,” Electrical power and
Energy systems, Vol. 19, No 2, pp 125-134, 1994.
10. K.S. Verma, S.N Singh and H.O. Gupta, “Location of unified
power flow controller for congestion management, “Electric
power systems research, Vol. 58, pp 89-96, 2001.
11. S. Gerbex, R. Cherkaoul and A.J Germond, “Optimal location
of multi-type FACTS devices in a power system by means of
genetic algorithms IEEE Trans Power Systems, Vol. 16, pp 537544, August 2001.
12. T.T Lie and W. Deng,”Optimal Flexible AC Transmission
systems (FACTS) devices allocation,”Electrical power & Energy
system, Vol.19, No.2, pp 125-134, 1997.
13. X. P. Wang, and L. P. Cao, Genetic Algorithms – Theory,
Application and Software Realization, Xi’an
Jiaotong
University, Xi’an, China,1998.
14. F.T. Lie, and W.Deng”optimal flexible AC Transmission
systems (FACTS) device allocation”, Electrical power and
Energy system,Vol.19,no 2,pp125-134,1997.
15. L. Gyugyl, C.D. Shauder and K. K. Sen,”static synchronous
series compensator A solid state approach to the
series
compensation of transmission line,” IEEE Transactions o power
delivery Vol.12, no. 3, 1997.
16. S. Gerbex, R.Cherkaoui, and A.J.Germund,”optimal location of
multi-type FACTS devices in a power
system by means of
genetic algorithms,” IEEE Trans power systems, Vol. 16,pp537544, August 2001.
17. X.P.Wang, and l.P Cao,”Genetic Algorithms Theory,
Application and Software Realization” ,Xi ’an Jiao tong
University Xi’an,China,1998
Appendix
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