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Frontiers in Energy

ISSN 2095-1701

ISSN 2095-1698(Online)

CN 11-6017/TK

Postal Subscription Code 80-972

2018 Impact Factor: 1.701

Front. Energy    2014, Vol. 8 Issue (3) : 290-296    https://doi.org/10.1007/s11708-014-0305-y
RESEARCH ARTICLE
Solution to economic dispatch problem with valve-point loading effect by using catfish PSO algorithm
K. MURALI,T. JAYABARATHI()
School of Electrical Engineering, VIT University, Vellore 632014, India
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Abstract

This paper proposes application of a catfish particle swarm optimization (PSO) algorithm to economic dispatch (ED) problems. The ED problems considered in this paper include valve-point loading effect, power balance constraints, and generator limits. The conventional PSO and catfish PSO algorithms are applied to three different test systems and the solutions obtained are compared with each other and with those reported in literature. The comparison of solutions shows that catfish PSO outperforms the conventional PSO and other methods in terms of solution quality though there is a slight increase in computational time.

Keywords economic dispatch (ED)      valve point loading      catfish particle swarm optimization (PSO)      optimization     
Corresponding Author(s): T. JAYABARATHI   
Issue Date: 09 September 2014
 Cite this article:   
K. MURALI,T. JAYABARATHI. Solution to economic dispatch problem with valve-point loading effect by using catfish PSO algorithm[J]. Front. Energy, 2014, 8(3): 290-296.
 URL:  
https://academic.hep.com.cn/fie/EN/10.1007/s11708-014-0305-y
https://academic.hep.com.cn/fie/EN/Y2014/V8/I3/290
AlgorithmsBest results/($·h-1)Mean results/($·h-1)
CEP [11]8234.078235.97
FEP [11]8234.078234.24
MFEP [11]8234.088234.71
IFEP [11]8234.078234.16
EP [19]8234.078234.16
EP-SQP [19]8234.078234.09
PSO-SQP [19]8234.078234.72
Firefly [16]8234.078234.08
SPSO [20]8234.078234.18
QPSO [20]8234.078234.10
PSO8234.078235.21
Catfish PSO8234.078236.52
Tab.1  Comparison of best and mean results for 3-unit test system
Catfish PSOPSO
P1/MW300.2643300.2635
P2/MW400.0000400.0000
P3/MW149.7356149.7364
Total generation/MW850850
Cost/($·h-1)8234.0738234.073
Mean time/s0.0640.063
Tab.2  Comparison of best results between catfish PSO and PSO for the 3-unit test system
Evaluation methodRange of cost/$
8234–82368238–82408240–82428242–8244Above 8244
PSO328253
Catfish PSO346163
Tab.3  Relative frequency of convergence for 50 trials for test case 1
Fig.1  Convergence characteristics of catfish PSO and PSO for the 3-unit test system
AlgorithmsBest results/($·h-1)Mean results/($·h-1)
CEP [11]18048.2118190.32
FEP [11]18018.0018200.79
MFEP [11]18028.0918192.00
IFEP [11]17994.0718127.06
EP [19]17,994.0718127.06
EP–SQP [19]17,991.0318106.93
PSO–SQP [20]17,969.9318029.99
SPSO [20]17988.1518102.48
QPSO [20]17969.0118075.11
PSO17974.6218042.42
Catfish PSO17969.9918039.28
Tab.4  Comparison of best and mean results for the 13-unit test system
Catfish PSOPSO
P1/MW5555
P2/MW149.904224.404
P3/MW224.82298.394
P4/MW109.881109.614
P5/MW109.88360
P6/MW109.87160
P7/MW109.87360
P8/MW109.90960
P9/MW109.875109.531
P10/MW77.42340
P11/MW4040
P12/MW5555
P13/MW538.561628.054
Total generation/MW18001800
Cost/($·h-1)1796917974
Mean Time/s3.643.59
Tab.5  Comparison of best results between catfish PSO and PSO for the 13-unit test system
Evaluation methodRange of cost/$
17950–1800018000–1805018050–1810018100–18150Above 18150
PSO348125
Catfish PSO366224
Tab.6  Relative frequency of convergence for 50 trials for case 2
Fig.2  Convergence characteristics of Catfish PSO and PSO for the 13-unit test system
Catfish PSOPSOCatfish PSOPSO
P1/MW113.320114.000P21/MW540.405523.433
P2/MW114.000110.687P22/MW533.392523.567
P3/MW97.794101.035P23/MW521.444524.319
P4/MW179.557179.931P24/MW528.949530.827
P5/MW95.31887.340P25/MW550.000523.255
P6/MW139.548140.000P26/MW550.000523.931
P7/MW299.984300.000P27/MW10.48010.652
P8/MW288.840288.376P28/MW10.08510.000
P9/MW291.817284.568P29/MW14.75510.410
P10/MW130.196130.000P30/MW95.59789.925
P11/MW94.36794.293P31/MW189.837189.577
P12/MW94.03294.632P32/MW189.841189.751
P13/MW512.629511.250P33/MW190.000190.000
P14/MW394.417396.575P34/MW200.000200.000
P15/MW306.679392.212P35/MW198.941166.112
P16/MW93.418305.163P36/MW192.612200.000
P17/MW490.850486.266P37/MW110.000109.674
P18/MW489.754494.290P38/MW110.000109.612
P19/MW511.660513.080P39/MW110.000110.000
P20/MW512.028512.479P40/MW214.730214.730
Catfish PSOPSO
Total generation/MW1050010500
Cost($·h-1)121683.70121818.04
Mean time/s8.548.23
Tab.7  Comparison of best and mean results for the 40-unit test system
AlgorithmsBest resultsMean results
CEP [11]123488.29124793.48
FEP [11]122679.71127245.59
MFEP [11]122647.57125356.47
IFEP [11]122624.35125740.63
EP [19]122624.35123382.00
EP–SQP [19]122323.97122379.63
PSO–SQP [20]122094.67122245.25
SPSO [20]121787.39122474.40
QPSO [20]121448.21122225.07
PSO121818.04122122.36
Catfish PSO121683.70121989.62
Tab.8  Comparison of best results between catfish PSO and PSO for the 40-unit test system
Evaluation methodRange of cost/$
121400–121800121800–122200122200–122600122600–123000Above 123000
PSO432842
Catfish PSO537611
Tab.9  Relative frequency of convergence for 50 trials for case 3
Fig.3  Convergence characteristics of catfish PSO and PSO for the 40-unit test system
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