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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

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Frontiers in Energy  0, Vol. Issue (): 75-89   https://doi.org/10.1007/s11708-012-0222-x
  RESEARCH ARTICLE 本期目录
Solving multi-objective optimal power flow problem considering wind-STATCOM using differential evolution
Solving multi-objective optimal power flow problem considering wind-STATCOM using differential evolution
Belkacem MAHDAD(), K. SRAIRI
LMSE Laboratory, Department of Electrical Engineering, University of Biskra, Biskra 07000, Algeria
 全文: PDF(587 KB)   HTML
Abstract：

In this paper, a simple strategy based differential evolution was proposed for solving the problem of multi-objective environmental optimal power flow considering a hybrid model (Wind-Shunt-FACTS). The DE algorithm optimized simultaneously a combined vector control based active power of wind sources and reactive power of multi STATCOM exchanged with the electrical power system to minimize fuel cost and emissions. The proposed strategy was examined and applied to the standard IEEE 30-bus with smooth cost function to solve the problem of security environmental economic dispatch considering multi distributed hybrid model based wind and STATCOM controllers. In addition, the proposed approach was validated on a large practical electrical power system 40 generating units considering valve point effect. Simulation results demonstrate that choosing the installation of multi type of FACTS devices in coordination with many distributed wind sources is a vital research area.
Key words： differential evolution    multi-objective function    optimal power flow    economic dispatch    valve point effect    environment    wind source    STATCOM
收稿日期: 2012-09-09      出版日期: 2013-03-05
Corresponding Author(s): MAHDAD Belkacem,Email:bemahdad@yahoo.fr   
 引用本文:   
. Solving multi-objective optimal power flow problem considering wind-STATCOM using differential evolution[J]. Frontiers in Energy, 0, (): 75-89.
Belkacem MAHDAD, K. SRAIRI. Solving multi-objective optimal power flow problem considering wind-STATCOM using differential evolution. Front Energ, 0, (): 75-89.
 链接本文:  
https://academic.hep.com.cn/fie/CN/10.1007/s11708-012-0222-x
https://academic.hep.com.cn/fie/CN/Y0/V/I/75
Fig.1  
Fig.2  
Fig.3  
Fig.4  
Fig.5  
Fig.6  
Variables Pgmin?Pgmax?Minimum fuel costCombined minimum fuel cost & minimumβ emissionMinimum emissionβ
Pg1/MW40200177.3000133.100063.9600
Pg2/MW208048.750057.120067.7600
Pg5/MW155021.360024.060050.0000
Pg8/MW103521.020035.000035.0000
Pg11/MW103011.850020.010030.0000
Pg13/MW124012.000020.430040.0000
Generation cost/($·h-1)799.9208815.6620944.9071
Emission/(t·h-1)0.36680.27190.2049
Total cost/($·h-1)1001.9965.38651057.7
Power loss/MW8.8766.3213.319
Tab.1  
Fig.7  
Minimum fuel costCombined minimum fuel cost & minimumβ emissionMinimum Emission
FGA [31]DEFGA [31]DEFGA [31]DE
Generation cost/($·h-1)802.8856799.9208822.7461815.6620905.2959944.9071
Emission/(t·h-1)0.36450.36680.26620.27190.22650.2049
Total cost/($·h-1)1003.601001.9969.3318965.38651030.901057.7
Tab.2  
Fig.8  
Fig.9  
Variables Pg?min?Pg?max?Minimumβ fuel costCombined minimum fuel cost & minimumβ emission Minimum emissionβ
Pg1/MW40200150.6200121.04044.15
Pg2/MW208046.530052.95050.65
Pg5/MW155020.640022.36050.00
Pg8/MW103515.810025.17035.00
Pg11/MW103010.050015.66030.00
Pg13/MW124012.000016.32040.00
Generation cost/($·h-1)678.6375688.1710831.8585
Emission/(t·h-1)0.30970.25990.1983
Total cost/($·h-1)849.1769831.2875941.0544
Power loss/MW7.9736.1042.396
Tab.3  
Fig.10  
Fig.11  
Fig.12  
Fig.13  
Fig.14  
Candidate buses
STATCOM Location101215172021232429
Q/MVAR40.35-16.77-9.81-19.34-1.96-19.981.254.87-4.18
Pw/MW3.923.924.014.064.184.203.973.873.87
∑i=1NWPwi/MW36 MW(12.7%), PD=283.4 MW
Tab.4  
Fig.15  
Unit No.Pgi/MWUnit No.Pgi/MW
[QPSO][33][DEBBO][32]Our approach[QPSO][33][DEBBO][32]Our approach
1111.20110.7998110.805721523.28523.2794523.2793
2111.70110.7998110.800022523.28523.2794523.2802
397.4097.399997.400523523.29523.2794523.2818
4179.73179.7331179.737224523.28523.2794523.2797
590.1487.957687.802525523.29523.2794523.2782
6140.00140.000140.000026523.28523.2794523.2821
7259.60259.5997259.59972710.0110.0010.0000
8284.80284.5997284.59992810.0110.0010.0000
9284.84284.5997284.60092910.0010.0010.0000
10130.00130.000130.00003088.4797.00087.7968
11168.80168.799894.000031190.00190.000190.0000
12168.8094.00094.000032190.00190.000190.0000
13214.76214.7598214.761233190.00190.000190.0000
14304.53394.2794394.278334164.91164.7998164.8019
15394.28394.2794394.277335165.36200.00194.3764
16394.28304.5196394.278636167.19200.00200.0000
17489.28489.2794489.280237110.00110.0000110.0000
18489.28489.2794489.279938107.01110.0000110.0000
19511.28511.2794511.281939110.00110.0000110.0000
20511.28511.2794511.278940511.36511.2794511.2809
TP/MW105001050010500
TC/($·h-1)121448.21121420.89121412.8684
Notes: TP—Total power generation; TC—Total cost
Tab.5  
Methods: Refs. [17,24,32,33,34]Minimum cost/($·h-1)Worst cost/($·h-1)Average time/s
CEP123488.29//
FEP122679.71//
MFEP122647.57//
IFEP122624.35//
EGA122022.96/12.892
FIA121823.80/12.854
SPSO121787.39/5.055
DEBBO121420.89//
QSPO121448.21/5.374
Proposed approach 121412.8684121421.069910.380
Tab.6  
Fig.16  
Unit No.Pgi/MW
Run 1Run 2Run 3Run 4Run 5Run 6Run 7
1110.7963110.7940110.8000110.7984110.8052110.7820110.9377
2110.8049110.8006110.8055110.8436110.8032110.8431110.8368
397.400997.399897.400997.413597.423397.398397.4378
4179.7327179.7304179.7309179.7382179.7168179.7446179.7518
587.805787.805387.801287.799087.801187.818087.8414
6140.0000140.0000140.0000140.0000140.0000140.0000140.0000
7259.5958259.6012259.5989259.5933259.6069259.5970259.6015
8284.6068284.6006284.5996284.6081284.6016284.5995284.7250
9284.6058284.6012284.5988284.5857284.5938284.5995284.5836
10130.0000130.0000130.0000130.0000130.0000130.0000130.0000
1194.000094.000094.000094.000094.000094.000094.0000
1294.000094.000094.000094.000094.000094.000094.0000
13214.7560214.7566214.7569214.7662214.7753214.7593214.8026
14394.2778394.2791394.2782394.2876394.2645394.2559394.2727
15394.2791394.2790394.2775?394.2808394.2633394.2793394.2711
16394.2782394.2663394.2793394.2850394.2705394.2917394.2526
17489.2766489.2794489.2892489.2808489.2723489.2787489.2756
18489.2819489.2780489.2802489.2773489.2811489.2810489.2585
19511.2807511.2777511.2822511.2867511.2796511.2670511.2920
20511.2798511.2841511.2793511.2783511.2654511.2745511.2932
21523.2807523.2780523.2803523.2830523.2772523.2836523.3908
22523.2793523.2870523.2820523.2858523.2911523.2968523.3102
23523.2785523.2777523.2843523.2856523.2787523.2832523.2867
24523.2765523.2793523.2779523.2801523.2889523.2867523.3025
25523.2861523.2818523.2785523.2904523.2880523.3038523.3029
26523.2831523.2798523.2795523.2814523.2835523.2674523.2898
2710.000010.000010.000010.000010.000010.000010.0000
2810.000010.000010.000010.000010.000010.000010.0000
2910.000010.000010.000010.000010.000010.000010.0000
3087.800187.800687.802187.806487.802187.809288.1814
31190.0000190.0000190.0000190.0000190.0000190.0000190.0000
32190.0000190.0000190.0000190.0000190.0000190.0000190.0000
33190.0000190.0000190.0000190.0000190.0000190.0000190.0000
34164.7989164.7998164.7978164.7979164.7962164.8770164.7991
35194.3753194.4032200.0000194.2815200.0000200.0000193.3452
36200.0000200.0000194.3798200.0000194.3876194.2448200.0000
37110.0000110.0000110.0000110.0000110.0000110.0000110.0000
38110.0000110.0000110.0000110.0000110.0000110.0000110.0000
39110.0000110.0000110.0000110.0000110.0000110.0000110.0000
40511.2827511.2796511.2794511.2854511.2831511.2781511.3574
Cost/($·h-1)121413.09953121413.0315121412.940121414.0199121414.217121414.9470121421.0699
Tab.7  
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