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Frontiers in Energy

ISSN 2095-1701

ISSN 2095-1698(Online)

CN 11-6017/TK

邮发代号 80-972

2019 Impact Factor: 2.657

Frontiers in Energy  2014, Vol. 8 Issue (4): 449-458   https://doi.org/10.1007/s11708-014-0316-8
  本期目录
Artificial bee colony optimization for economic dispatch with valve point effect
Yacine LABBI1,*(),Djilani Ben ATTOUS1,Belkacem MAHDAD2
1. Department of Electrical Engineering, University of El-Oued, El-Oued 39014, Algeria
2. Department of Electrical Engineering, University of Biskra, Biskra 07000, Algeria
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Abstract

In recent years, various heuristic optimization methods have been proposed to solve economic dispatch (ED) problem in power systems. This paper presents the well-known power system ED problem solution considering valve-point effect by a new optimization algorithm called artificial bee colony (ABC). The proposed approach has been applied to various test systems with incremental fuel cost function, taking into account the valve-point effects. The results show that the proposed approach is efficient and robust when compared with other optimization algorithms reported in literature.

Key wordsartificial bee colony (ABC) algorithm    economic dispatch (ED)    valve-point effect    optimization
收稿日期: 2013-10-18      出版日期: 2015-01-09
Corresponding Author(s): Yacine LABBI   
 引用本文:   
. [J]. Frontiers in Energy, 2014, 8(4): 449-458.
Yacine LABBI,Djilani Ben ATTOUS,Belkacem MAHDAD. Artificial bee colony optimization for economic dispatch with valve point effect. Front. Energy, 2014, 8(4): 449-458.
 链接本文:  
https://academic.hep.com.cn/fie/CN/10.1007/s11708-014-0316-8
https://academic.hep.com.cn/fie/CN/Y2014/V8/I4/449
Fig.1  
Units P min ? i P max ? i a b c e f
123 10050100 600200400 0.0015620.0048200.001940 7.927.977.85 56178310 300150200 0.03150.0630.042
Tab.1  
Units Proposed ABC
1 power output/MW2 power output/MW3 power output/MWTotal power output/MWTotal cost/($·h–1) 300.2656149.7344400.0000850.0008234.07245
Tab.2  
Method P1/MW P2/MW P3/MW PD/MW Cost/($·h–1)
GA [18]EP [18]EP-SQP [18]PSO [18]PSO-SQP [18]GAB [19]GAF [19]CEP [19]FEP [19]MFEP [19]IFEP [19]PS [9]GSA [20]Proposed ABC 398.700300.264300.267300.268300.267300.2663300.2102300.2656 50.100149.736149.733149.732149.733149.7331149.7953149.7344 399.600400.000400.000400.000400.000399.9996399.9958400.0000 848.400850.000850.000850.000850.000849.9990850.0013850.000 8222.078234.078234.078234.078234.078234.088234.078234.078234.078234.088234.078234.058234.18234.07245
Tab.3  
Fig.2  
Fig.3  
Units P min ? i P max ? i a b c e f
12345678910111213 00060606060606040405555 680360360180180180180180180120120120120 0.000280.000560.000560.003240.003240.003240.003240.003240.003240.002840.002840.002840.00284 8.108.108.107.747.747.747.747.747.748.608.608.608.60 550309307240240240240240240126126126126 300200150150150150150150150100100100100 0.0350.0420.0420.0630.0630.0630.0630.0630.0630.0840.0840.0840.084
Tab.4  
Units ?Proposed ABC ?Units ?Proposed ABC
1 power output/MW2 power output/MW3 power output/MW4 power output/MW5 power output/MW6 power output/MW7 power output/MW8 power output/MW ?628.2772?148.8823?223.6160?60.0000?109.8531?109.8395?109.8605?109.8550 ?9 power output/MW?10 power output/MW?11 power output/MW?12 power output/MW?13 power output/MW?Total power output/MW?Total cost/($·h–1) ?109.8263?40.0000?40.0000?55.0000?55.00001800.0099?17962.4279
Tab.5  
Units ?Proposed GSA ?Units ?Proposed GSA
1 power output/MW2 power output/MW3 power output/MW4 power output/MW5 power output/MW6 power output/MW7 power output/MW8 power output/MW ?628.3119?298.9825?295.7710?159.7329?159.7318?159.7293?159.7324?159.7277 ?9 power output/MW?10 power output/MW?11 power output/MW?12 power output/MW?13 power output/MW?Total power output/MW?Total cost/($·h–1) ?159.7309?77.2108?77.0372?92.2275?92.0833?2520.0092?24166.2199
Tab.6  
Method ?Total cost/($·h–1) ?Method ?Total cost/($·h–1)
CEP [19]PSO [18]MFEP [19]FEP [19]IFEP [19]EP-SQP [18]HDE [21]CGA-MU [22]PSO-SQP [18]PS [9] ?18048.21?18030.72?18028.09?18018.00?17994.07?17991.03?17975.73?17975.34?17969.93?17969.17 ?UHGA [2]?QPSO [14]?IGA-MU [22]?ST-HDE [21]?HGA [7]?HQPSO(5) [8]?DE [23]?GSA [20]?Proposed ABC ?17964.81?17964?17963.98?17963.89?17963.83?17963.9571?17963.83?17960.3684?17962.4279
Tab.7  
Fig.4  
Fig.5  
Method Total cost/($·h–1) ?Method Total cost/($·h–1)
SA [18]GA [18]GA-SA [18]EP-SQP [18]PSO-SQP [18]UHGA [2]GA-MU [24] 24970.9124398.2324275.7124266.4424261.0524172.2524170.755 ?IGA-MU [24]?HGA [7]?EDSA [19]?DE [23]?GSA [20]?Proposed 24169.97924169.9224169.9224169.917724164.25135724166.2199
Tab.8  
Fig.6  
Fig.7  
Generator power output ABC NPSO-LRS [25] NPSO [25] MDE [26] CBPSO-RVM [27] FAPSO-NM [28]
Pg1/MWPg2/MWPg3/MWPg4/MWPg5/MWPg6/MWPg7/MWPg8/MWPg9/MWPg10/MWPg11/MWPg12/MWPg13/MWPg14/MWPg15/MWPg16/MWPg17/MWPg18/MWPg19/MWPg20/MWPg21/MWPg22/MWPg23/MWPg24/MWPg25/MWPg26/MWPg27/MWPg28/MWPg29/MWPg30/MWPg31/MWPg32/MWPg33/MWPg34/MWPg35/MWPg36/MWPg37/MWPg38/MWPg39/MWPg40/MWTotal cost/($·h–1) 110.7944110.791397.4473179.741787.8268139.9897259.5761284.5962284.5294130.0033168.790394.0010215.4183394.2843394.2274394.1741489.2802489.2863511.2606511.2471523.3126523.2619523.2069523.2790523.2828523.282810.003510.060110.006388.0050189.8676189.9970179.4734164.8527164.8280164.8093109.9733109.9999109.9544511.2777121479.6467 113.9761113.998697.4241179.732789.6511105.4044259.7502288.4534284.646204.812168.831194214.7663394.2852304.5187394.2811489.2807489.2832511.2845511.3049523.2916523.2853523.2797523.2994523.2865523.29361010.00011089.0139190190190199.9998165.1397172.027511011093.0962511.2996121664.43 113.9891113.633497.55180.005997140300300284.5797130.0517243.7131169.0104125393.9662304.7586304.512489.6024489.6087511.7903511.2624523.3274523.2196523.4707523.0661523.3978523.289710.020810.092710.062188.9456189.9951190190165.9825172.4153191.2978109.9893109.9521109.8733511.5671121704.73 110.831110.81597.399179.73487.808140259.6284.604284.601130168.799168.799214.759394.28394.28304.519489.279489.28511.28511.279523.279523.28523.28523.28523.281523.27910101092.645190190189.999164.831164.802164.805109.999109.999109.999511.278121414.79 11411497.4859179.733197140300300286.00791309494214.7598304.5196394.2794394.2794489.2794489.2794511.2794511.2794523.2796523.2794523.2797523.2802523.2795523.279410101097190190190200166.8603200110110110511.2794121555.32 111.38110.9397.41179.3389.22140259.62284.66284.66130168.82168.82214.75394.28304.54394.3489.29489.29511.28511.29523.33523.48523.33523.33523.33523.3310101088.7190190190165166165110110110511.3121418.3
Tab.9  
Method Minimum cost/($·h–1) Mean cost/($·h–1) Maximum cost/($·h–1) Mean time/s
CEP [19]FEP [19]MFEP [19]IFEP [19]NPSO-LRS [25]MDE [26]GA [26]CBPSO-RVM [27]PS [29]FAPSO-NM [28]EP-SQP [30]PSO [30]PSO-SQP [30]MPSO [31]ESO [32]DEC(2)-SQP(1) [33]TM [34]APSO [35]TS [36]ACO [36]ABC 123488.29122679.71122647.57122624.35121664.43121414.79121996.40121555.32121415.14121418.3122323.97123930.45122094.67122252.27122122.16121741.98122477.78121663.52122288.38121811.37121479.6467 124793.5124119.4123489.7123382.0122209.31121418.44123807.97122281.14122332.7121418.80122379.6124155122245.3122524.1122295.1123078.2122153.67122590.89121930.58121984.24 126902.9127245.6124356.5125740.6122981.59121466.04122919.77123094.98125486.3121419.8123143.1122839.3124693.8122912.39122424.81122048.06122137.42 1956.91039.12196.11167.319.8-320.3142.9840997.73933.39733.9714.2694.285.05238.3592.5416.52
Tab.10  
Fig.8  
Fig.9  
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