- Email: [email protected]
economic hydrothermal scheduling” by A. Ahmadi et al. [Electr. Power Syst. Res. 116 (2014) 117–127]”
Electric Power Systems Research 127 (2015) 348–350
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Discussion Reply to “Discussion on “Short-term environmental/economic hydrothermal scheduling” by A. Ahmadi et al. [Electr. Power Syst. Res. 116 (2014) 117–127]”
a r t i c l e
i n f o
a b s t r a c t
Keywords: Environmental/economic hydrothermal Fuzzy satisfying method ∈-Constraint technique
This short communication is the reply to “Discussion on”Short-term environmental/economic hydrothermal scheduling” by A. Ahmadi, et al. [Electric Power Syst. Res. 116 (2014) 117–127]”. © 2015 Published by Elsevier B.V.
First of all, the authors are grateful to Chen and Zheng for their deep consideration of the original paper [1]. As they have correctly mentioned, the date of the mentioned test case can be found in [2]. Table 1 represents the calculated cost of each time interval by [3] and our proposed method. It seems that Chen, and Zheng [3] supposed that the argument of sinusoidal part of the cost function, sin{fsi ∗ (PsiMin − Psit )} e.g. fsi ∗ (PsiMin − Psit ) is in Radians while we supposed that it is based on
Degree. Making such assumptions, the values reported by Chen and Zheng [3] and us [1] are correct. It is worth-mentioning that the simulations have been done in the original paper [1], based on this assumption that the unit of fsi is Degree/MW. With this assumption, the reported values in [1] are correct, but if we suppose that the unit of fsi is Radians/MW, the reported values must be modified based on new assumptions which has been done as follows. Fig. 1 indicates the optimal Pareto front derived from the presented method.
Table 1 The recalculated cost of each time interval. Hour
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Thermal generations in MW Ps1t
Ps2t
Ps3t
137.3100 146.9400 122.9800 108.3600 108.8900 140.7500 171.3200 175.0000 175.0000 175.0000 175.0000 175.0000 175.0000 167.2900 160.1700 173.0700 168.1500 175.0000 170.8800 162.5500 119.6300 104.4400 101.9300 87.9600
174.7200 186.5800 156.9400 138.7100 139.3700 178.9600 216.3200 229.9800 256.0100 243.0100 246.4200 269.2600 248.9000 211.4400 202.7800 218.4300 212.4800 241.3000 215.7800 205.6800 152.7700 133.8200 130.6800 113.1700
150.5100 159.0000 138.0000 125.3700 125.8300 153.5300 180.9800 191.5400 212.8500 201.9900 204.7900 224.4900 206.8500 177.2800 170.8200 182.5800 178.0700 200.5900 180.5700 172.9800 135.1000 122.0100 119.8600 107.9200
DOI of original article: http://dx.doi.org/10.1016/j.epsr.2015.04.021. http://dx.doi.org/10.1016/j.epsr.2015.05.009 0378-7796/© 2015 Published by Elsevier B.V.
Cost [3]
Our method
1916.6633 2015.5313 1687.2108 1496.2810 1504.6877 1958.7498 2125.3651 2256.8836 2359.6862 2338.7985 2350.2745 2321.6227 2355.9219 2073.7055 2061.4200 2145.7061 2085.2325 2331.4478 2119.9415 2060.4994 1652.0995 1431.3144 1396.6833 1454.3884 Total cost: 47,500.1148 (S)
1555.3105 1639.1862 1431.7923 1307.5155 1311.9951 1585.1651 1855.2667 1934.9273 2071.2365 2002.2076 2020.1097 2143.9551 2033.2259 1819.1484 1755.7493 1870.9458 1826.8426 1993.2594 1851.2798 1776.9143 1403.1738 1274.5376 1253.4634 1137.0363 Total cost: 40,854.2442 ($)
Discussion / Electric Power Systems Research 127 (2015) 348–350
349
Table 2 Result of different methods. Method
[2]
Cost ($) Emission (lbs)
[4]
47,906.000 26,234.000
[5]
44,914.000 19,615.000
The most compromise solution derived from -constraint technique and lexicographic optimization along with the solutions reported by Refs. [2,4–6] is represented in Table 2, while we suppose that the unit of fsi is Radians/MW. As it can be seen in Table 2, the results obtained from the proposed problem are better than those reported in [2,4–6]. Table 3 shows the details of the solution using the proposed method,
[6]
43,507.000 18,183.000
Proposed method
43,593.000 16,204.000
43,199.719 16,202.830
while all constraints are satisfied. Table 3 would be the evidence for the effectiveness of the proposed method for solving combined economic emission scheduling problem of hydrothermal systems. It can be observed that all constraints of the problem have been thoroughly satisfied. The Authors are confident that the results presented in the paper are correct and valid.
Table 3 The details of the solution using the proposed method. Hour
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hour
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Water discharge rates (×104 m3 )
Hydro generations in MW
Qh1t
Qh2t
Qh3t
Qh4t
Ph1t
Ph2t
Ph3t
Ph4t
8.807536685 7.058337226 7.366174251 7.060309320 6.918565311 5.005621485 9.997654235 9.711662494 9.994350491 9.640777752 9.955990697 9.270126740 9.761069454 9.618788665 9.283035705 9.114550946 9.319215497 9.075571949 8.920127901 9.030299253 5.090233942 5.000000000 5.000000000 5.000000000
6.000000000 6.000000000 6.000000000 6.000000000 6.000000000 6.000000000 7.333094225 7.231100774 8.593013980 7.792906255 8.508001028 7.757169717 8.880120150 8.999548220 8.916127147 9.140430116 9.873889433 10.113016590 10.798621190 11.691118100 9.371937136 9.994411369 10.944601900 10.594605250
22.955567970 24.379574200 22.964688890 21.099553710 19.222358220 17.875222540 16.532009540 16.235599110 17.061694340 17.429976850 17.348124770 17.955572470 18.316370340 18.651402760 18.376589300 17.415961130 16.124577680 15.832816990 15.499914450 15.097883160 12.106352020 12.655280110 13.101697110 13.527593810
6.000000000 6.000000000 6.000000000 6.000000000 6.000000000 6.000000000 12.328815380 13.700563070 16.195625790 17.071961290 16.532009540 16.235599110 17.061694340 17.429976850 17.348124770 17.955572470 18.316370340 18.651402760 19.825985040 20.000000000 18.965720470 19.556037210 20.000000000 20.000000000
80.298097330 69.644375290 71.969955030 69.797910600 68.550965160 53.458686120 86.959304760 85.349409150 86.704203040 85.444690850 87.637125110 84.357325390 87.272960500 87.206739280 85.835349610 85.094589140 86.171549470 84.545197790 83.181364710 83.003973460 54.723495130 54.301800000 54.705000000 55.020000000
50.164000000 51.296000000 52.934000000 54.500000000 55.504000000 55.994000000 64.504130850 63.721326590 68.894675790 67.894633460 72.442407640 68.049002150 74.217437640 74.877241860 74.462214430 75.071819110 77.227251390 75.914464510 76.555742470 77.562103720 67.261211070 69.594987970 71.634153780 68.299387260
24.845959310 8.7419245970 13.803070600 22.161640880 30.087775120 35.069168350 39.060592450 38.549735500 36.147259050 35.216846740 35.857224520 34.498703100 34.603674790 34.190788290 36.126897870 40.650034220 45.684216730 47.751543680 49.677592540 51.819263350 55.764020380 57.876097150 58.843953730 58.958700940
129.026880000 125.743680000 121.625280000 115.822080000 131.664231700 146.888545200 232.837929600 253.106456200 278.252640400 286.008253500 281.741139600 279.321825400 285.928802000 288.737907100 288.120841500 292.601287000 295.154183700 297.452502800 303.482568200 301.837090900 292.583575600 292.290980600 289.916320900 284.400000000
Volume (×104 m3 )
Thermal generations in MW
Vh1t
Vh2t
Vh3t
Vh4t
Ps1t
Ps2t
Ps3t
101.192463300 103.134126100 103.767951800 103.707642500 102.789077200 104.783455700 102.785801500 102.074139000 102.079788500 103.439010700 105.483020100 106.212893300 107.451823900 109.833035200 111.549999500 112.435448500 112.116233000 111.040661100 109.120533200 106.090233900 108.000000000 111.000000000 115.000000000 120.000000000
82.000000000 84.000000000 87.000000000 90.000000000 92.000000000 93.000000000 91.666905770 91.435805000 91.376503600 92.583597350 93.075596320 93.318426600 92.438306450 92.438758230 92.522631090 91.382200970 88.508311540 84.395294950 80.596673760 76.905555650 76.533618520 75.539207150 72.594605250 70.000000000 Cost ($)
155.144432000 138.964857800 128.807705600 122.766489100 119.910305200 119.095392000 118.481947700 115.251970100 115.187930000 115.802709900 116.680036400 118.424543000 121.857069600 123.983794700 126.125444500 129.208392200 133.366398500 137.564259600 141.523990700 146.375568900 155.302361400 164.476001700 169.155656700 170.000000000 43,199.718837544
116.800000000 113.200000000 108.800000000 102.800000000 119.755568000 138.135142200 148.771015700 156.170006300 159.196738700 160.000000000 160.000000000 160.000000000 160.000000000 160.000000000 160.000000000 160.000000000 160.000000000 160.000000000 158.550604300 155.966565400 153.125422600 149.402202400 144.902116800 140.000000000
175.000000000 175.000000000 175.000000000 123.050670000 119.525326700 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 121.268435700 110.232874800 102.673499400 Emission (lbs)
150.905271100 209.814231100 124.907906500 124.907907600 124.907911200 193.886364200 209.815883600 209.815819900 215.481641400 290.115272700 217.802524200 282.341956400 223.457544800 212.922339000 209.875937700 209.815819200 212.969081300 209.816711000 209.815812200 210.694605800 124.907909200 124.907910300 124.907909700 124.907910200 16,202.830000000
139.759792300 139.759789000 139.759787900 139.759790900 139.759790100 139.703236000 141.822158800 184.457252600 229.519580300 140.320302800 229.519578900 226.431187500 229.519580200 157.064984500 140.578758800 181.766451300 157.793717400 229.519580200 172.286919900 150.082962700 139.759788700 139.759788300 139.759787000 105.740502200
Ph +
Ps
750.000000000 780.000000000 700.000000000 650.000000000 670.000000000 800.000000000 950.000000000 1010.000000000 1090.000000000 1080.000000000 1100.000000000 1150.000000000 1110.000000000 1030.000000000 1010.000000000 1060.000000000 1050.000000000 1120.000000000 1070.000000000 1050.000000000 910.000000000 860.000000000 850.000000000 800.000000000
350
Discussion / Electric Power Systems Research 127 (2015) 348–350
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[4] K.K. Mandal, N. Chakraborty, Short-term combined economic emission scheduling of hydrothermal power systems with cascaded reservoirs using differential evolution, Energy Convers. Manage. 50 (1) (2009) 97–104. [5] S. Lu, C. Sun, Z. Lu, An improved quantum-behaved particle swarm optimization method for short-term combined economic emission hydrothermal scheduling, Energy Convers. Manage. 51 (3) (2010) 561–571. [6] Y. Lu, J. Zhou, H. Qin, Y. Wang, Y. Zhang, A hybrid multi-objective cultural algorithm for short-term environmental/economic hydrothermal scheduling, Energy Convers. Manage. 52 (5) (2011) 2121–2134.
17000
Emission (lbs)
16800 16600 16400 16200 16000 15800 15600 15400 40000
42000
44000
46000
48000
50000
Cost ($) Fig. 1. The optimal Pareto front derived using the presented method.
References [1] M.R. Norouzi, A. Ahmadi, A.M. Sharaf, A.E. Nezhad, Short-term environmental/economic hydrothermal scheduling, Electr. Power Syst. Res. 116 (2014) 117–127. [2] M. Basu, An interactive fuzzy satisfying method based on evolutionary programming technique for multiobjective short-term hydrothermal scheduling, Electr. Power Syst. Res. 69 (2004) 277–285. [3] J.J. Chen, J.H. Zheng, Discussion on “Short-term environmental/economic hydrothermal scheduling”, Electr. Power Syst. Res. 116 (2015) 117–127.
Mohammad Reza Norouzi a Abdollah Ahmadi b Adel M. Sharaf c,∗ Ali Esmaeel Nezhad d a Department of Electrical Engineering, Islamic Azad University, Lamerd Branch, Lamerd, Iran b The Australian Energy Research Institute and the School of Electrical Engineering and Telecommunications, University of New South Wales (UNSW Australia), Sydney 2052, NSW, Australia c Life Senior Member IEEE, Sharaf Energy Systems, Inc., Fredericton, NB, Canada d Department of Electrical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran ∗ Corresponding
author. Tel.: +1 506 453 4561. E-mail addresses: [email protected], [email protected] (A.M. Sharaf). Available online 4 June 2015
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Discussion Reply to “Discussion on “Short-term environmental/economic hydrothermal scheduling” by A. Ahmadi et al. [Electr. Power Syst. Res. 116 (2014) 117–127]”
a r t i c l e
i n f o
a b s t r a c t
Keywords: Environmental/economic hydrothermal Fuzzy satisfying method ∈-Constraint technique
This short communication is the reply to “Discussion on”Short-term environmental/economic hydrothermal scheduling” by A. Ahmadi, et al. [Electric Power Syst. Res. 116 (2014) 117–127]”. © 2015 Published by Elsevier B.V.
First of all, the authors are grateful to Chen and Zheng for their deep consideration of the original paper [1]. As they have correctly mentioned, the date of the mentioned test case can be found in [2]. Table 1 represents the calculated cost of each time interval by [3] and our proposed method. It seems that Chen, and Zheng [3] supposed that the argument of sinusoidal part of the cost function, sin{fsi ∗ (PsiMin − Psit )} e.g. fsi ∗ (PsiMin − Psit ) is in Radians while we supposed that it is based on
Degree. Making such assumptions, the values reported by Chen and Zheng [3] and us [1] are correct. It is worth-mentioning that the simulations have been done in the original paper [1], based on this assumption that the unit of fsi is Degree/MW. With this assumption, the reported values in [1] are correct, but if we suppose that the unit of fsi is Radians/MW, the reported values must be modified based on new assumptions which has been done as follows. Fig. 1 indicates the optimal Pareto front derived from the presented method.
Table 1 The recalculated cost of each time interval. Hour
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Thermal generations in MW Ps1t
Ps2t
Ps3t
137.3100 146.9400 122.9800 108.3600 108.8900 140.7500 171.3200 175.0000 175.0000 175.0000 175.0000 175.0000 175.0000 167.2900 160.1700 173.0700 168.1500 175.0000 170.8800 162.5500 119.6300 104.4400 101.9300 87.9600
174.7200 186.5800 156.9400 138.7100 139.3700 178.9600 216.3200 229.9800 256.0100 243.0100 246.4200 269.2600 248.9000 211.4400 202.7800 218.4300 212.4800 241.3000 215.7800 205.6800 152.7700 133.8200 130.6800 113.1700
150.5100 159.0000 138.0000 125.3700 125.8300 153.5300 180.9800 191.5400 212.8500 201.9900 204.7900 224.4900 206.8500 177.2800 170.8200 182.5800 178.0700 200.5900 180.5700 172.9800 135.1000 122.0100 119.8600 107.9200
DOI of original article: http://dx.doi.org/10.1016/j.epsr.2015.04.021. http://dx.doi.org/10.1016/j.epsr.2015.05.009 0378-7796/© 2015 Published by Elsevier B.V.
Cost [3]
Our method
1916.6633 2015.5313 1687.2108 1496.2810 1504.6877 1958.7498 2125.3651 2256.8836 2359.6862 2338.7985 2350.2745 2321.6227 2355.9219 2073.7055 2061.4200 2145.7061 2085.2325 2331.4478 2119.9415 2060.4994 1652.0995 1431.3144 1396.6833 1454.3884 Total cost: 47,500.1148 (S)
1555.3105 1639.1862 1431.7923 1307.5155 1311.9951 1585.1651 1855.2667 1934.9273 2071.2365 2002.2076 2020.1097 2143.9551 2033.2259 1819.1484 1755.7493 1870.9458 1826.8426 1993.2594 1851.2798 1776.9143 1403.1738 1274.5376 1253.4634 1137.0363 Total cost: 40,854.2442 ($)
Discussion / Electric Power Systems Research 127 (2015) 348–350
349
Table 2 Result of different methods. Method
[2]
Cost ($) Emission (lbs)
[4]
47,906.000 26,234.000
[5]
44,914.000 19,615.000
The most compromise solution derived from -constraint technique and lexicographic optimization along with the solutions reported by Refs. [2,4–6] is represented in Table 2, while we suppose that the unit of fsi is Radians/MW. As it can be seen in Table 2, the results obtained from the proposed problem are better than those reported in [2,4–6]. Table 3 shows the details of the solution using the proposed method,
[6]
43,507.000 18,183.000
Proposed method
43,593.000 16,204.000
43,199.719 16,202.830
while all constraints are satisfied. Table 3 would be the evidence for the effectiveness of the proposed method for solving combined economic emission scheduling problem of hydrothermal systems. It can be observed that all constraints of the problem have been thoroughly satisfied. The Authors are confident that the results presented in the paper are correct and valid.
Table 3 The details of the solution using the proposed method. Hour
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hour
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Water discharge rates (×104 m3 )
Hydro generations in MW
Qh1t
Qh2t
Qh3t
Qh4t
Ph1t
Ph2t
Ph3t
Ph4t
8.807536685 7.058337226 7.366174251 7.060309320 6.918565311 5.005621485 9.997654235 9.711662494 9.994350491 9.640777752 9.955990697 9.270126740 9.761069454 9.618788665 9.283035705 9.114550946 9.319215497 9.075571949 8.920127901 9.030299253 5.090233942 5.000000000 5.000000000 5.000000000
6.000000000 6.000000000 6.000000000 6.000000000 6.000000000 6.000000000 7.333094225 7.231100774 8.593013980 7.792906255 8.508001028 7.757169717 8.880120150 8.999548220 8.916127147 9.140430116 9.873889433 10.113016590 10.798621190 11.691118100 9.371937136 9.994411369 10.944601900 10.594605250
22.955567970 24.379574200 22.964688890 21.099553710 19.222358220 17.875222540 16.532009540 16.235599110 17.061694340 17.429976850 17.348124770 17.955572470 18.316370340 18.651402760 18.376589300 17.415961130 16.124577680 15.832816990 15.499914450 15.097883160 12.106352020 12.655280110 13.101697110 13.527593810
6.000000000 6.000000000 6.000000000 6.000000000 6.000000000 6.000000000 12.328815380 13.700563070 16.195625790 17.071961290 16.532009540 16.235599110 17.061694340 17.429976850 17.348124770 17.955572470 18.316370340 18.651402760 19.825985040 20.000000000 18.965720470 19.556037210 20.000000000 20.000000000
80.298097330 69.644375290 71.969955030 69.797910600 68.550965160 53.458686120 86.959304760 85.349409150 86.704203040 85.444690850 87.637125110 84.357325390 87.272960500 87.206739280 85.835349610 85.094589140 86.171549470 84.545197790 83.181364710 83.003973460 54.723495130 54.301800000 54.705000000 55.020000000
50.164000000 51.296000000 52.934000000 54.500000000 55.504000000 55.994000000 64.504130850 63.721326590 68.894675790 67.894633460 72.442407640 68.049002150 74.217437640 74.877241860 74.462214430 75.071819110 77.227251390 75.914464510 76.555742470 77.562103720 67.261211070 69.594987970 71.634153780 68.299387260
24.845959310 8.7419245970 13.803070600 22.161640880 30.087775120 35.069168350 39.060592450 38.549735500 36.147259050 35.216846740 35.857224520 34.498703100 34.603674790 34.190788290 36.126897870 40.650034220 45.684216730 47.751543680 49.677592540 51.819263350 55.764020380 57.876097150 58.843953730 58.958700940
129.026880000 125.743680000 121.625280000 115.822080000 131.664231700 146.888545200 232.837929600 253.106456200 278.252640400 286.008253500 281.741139600 279.321825400 285.928802000 288.737907100 288.120841500 292.601287000 295.154183700 297.452502800 303.482568200 301.837090900 292.583575600 292.290980600 289.916320900 284.400000000
Volume (×104 m3 )
Thermal generations in MW
Vh1t
Vh2t
Vh3t
Vh4t
Ps1t
Ps2t
Ps3t
101.192463300 103.134126100 103.767951800 103.707642500 102.789077200 104.783455700 102.785801500 102.074139000 102.079788500 103.439010700 105.483020100 106.212893300 107.451823900 109.833035200 111.549999500 112.435448500 112.116233000 111.040661100 109.120533200 106.090233900 108.000000000 111.000000000 115.000000000 120.000000000
82.000000000 84.000000000 87.000000000 90.000000000 92.000000000 93.000000000 91.666905770 91.435805000 91.376503600 92.583597350 93.075596320 93.318426600 92.438306450 92.438758230 92.522631090 91.382200970 88.508311540 84.395294950 80.596673760 76.905555650 76.533618520 75.539207150 72.594605250 70.000000000 Cost ($)
155.144432000 138.964857800 128.807705600 122.766489100 119.910305200 119.095392000 118.481947700 115.251970100 115.187930000 115.802709900 116.680036400 118.424543000 121.857069600 123.983794700 126.125444500 129.208392200 133.366398500 137.564259600 141.523990700 146.375568900 155.302361400 164.476001700 169.155656700 170.000000000 43,199.718837544
116.800000000 113.200000000 108.800000000 102.800000000 119.755568000 138.135142200 148.771015700 156.170006300 159.196738700 160.000000000 160.000000000 160.000000000 160.000000000 160.000000000 160.000000000 160.000000000 160.000000000 160.000000000 158.550604300 155.966565400 153.125422600 149.402202400 144.902116800 140.000000000
175.000000000 175.000000000 175.000000000 123.050670000 119.525326700 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 175.000000000 121.268435700 110.232874800 102.673499400 Emission (lbs)
150.905271100 209.814231100 124.907906500 124.907907600 124.907911200 193.886364200 209.815883600 209.815819900 215.481641400 290.115272700 217.802524200 282.341956400 223.457544800 212.922339000 209.875937700 209.815819200 212.969081300 209.816711000 209.815812200 210.694605800 124.907909200 124.907910300 124.907909700 124.907910200 16,202.830000000
139.759792300 139.759789000 139.759787900 139.759790900 139.759790100 139.703236000 141.822158800 184.457252600 229.519580300 140.320302800 229.519578900 226.431187500 229.519580200 157.064984500 140.578758800 181.766451300 157.793717400 229.519580200 172.286919900 150.082962700 139.759788700 139.759788300 139.759787000 105.740502200
Ph +
Ps
750.000000000 780.000000000 700.000000000 650.000000000 670.000000000 800.000000000 950.000000000 1010.000000000 1090.000000000 1080.000000000 1100.000000000 1150.000000000 1110.000000000 1030.000000000 1010.000000000 1060.000000000 1050.000000000 1120.000000000 1070.000000000 1050.000000000 910.000000000 860.000000000 850.000000000 800.000000000
350
Discussion / Electric Power Systems Research 127 (2015) 348–350
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[4] K.K. Mandal, N. Chakraborty, Short-term combined economic emission scheduling of hydrothermal power systems with cascaded reservoirs using differential evolution, Energy Convers. Manage. 50 (1) (2009) 97–104. [5] S. Lu, C. Sun, Z. Lu, An improved quantum-behaved particle swarm optimization method for short-term combined economic emission hydrothermal scheduling, Energy Convers. Manage. 51 (3) (2010) 561–571. [6] Y. Lu, J. Zhou, H. Qin, Y. Wang, Y. Zhang, A hybrid multi-objective cultural algorithm for short-term environmental/economic hydrothermal scheduling, Energy Convers. Manage. 52 (5) (2011) 2121–2134.
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Cost ($) Fig. 1. The optimal Pareto front derived using the presented method.
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Mohammad Reza Norouzi a Abdollah Ahmadi b Adel M. Sharaf c,∗ Ali Esmaeel Nezhad d a Department of Electrical Engineering, Islamic Azad University, Lamerd Branch, Lamerd, Iran b The Australian Energy Research Institute and the School of Electrical Engineering and Telecommunications, University of New South Wales (UNSW Australia), Sydney 2052, NSW, Australia c Life Senior Member IEEE, Sharaf Energy Systems, Inc., Fredericton, NB, Canada d Department of Electrical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran ∗ Corresponding
author. Tel.: +1 506 453 4561. E-mail addresses: [email protected], [email protected] (A.M. Sharaf). Available online 4 June 2015