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Comment on “Bee colony optimization for combined heat and power economic dispatch” by M. Basu [Expert Systems with Applications 38 (2011) 13527–13531]
Expert Systems with Applications 39 (2012) 13073–13074
Contents lists available at SciVerse ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
Discussion
Comment on ‘‘Bee colony optimization for combined heat and power economic dispatch’’ by M. Basu [Expert Systems with Applications 38 (2011) 13527–13531] H.R. Abdolmohammadi ⇑, A. Kazemi Centre of Excellence for Power System Automation and Operation, Department of Electrical Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran
a r t i c l e
i n f o
Keywords: Cogeneration Combined heat and power economic dispatch Optimization
a b s t r a c t We comment on error in a recently published paper by M. Basu [Expert Systems with Applications 38 (2011) 13527–13531]. The optimization algorithm based on Benders decomposition has been applied to a test system and the results are compared with those of bee colony optimization, particle swarm optimization, real-coded genetic algorithm and evolutionary programing techniques. The numerical results demonstrate that the proposed method has more advantages than other methods in application. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Firstly, it must be stated that Basu presented an interesting algorithm for solving combined heat and power economic dispatch (CHPED) problems in Basu (2011). Unlike previous works on CHPED problems, which did not consider transmission loss, the above article considers the active power transmission loss. However, in the above-mentioned article, errors were found in the system data and the reported results. The cogeneration units and their cost functions were originally proposed by Guo et al. (1996). Therefore, in Appendix A.1 of Basu (2011), it is necessary for the cost function of sixth cogeneration unit:
Table 1 Results obtained from BCO, EP, PSO and RCGA (Table 1 of Basu (2011)).
P1 (MW) P2 (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) H5 (MWth) H6 (MWth) H5 (MWth) PL (MW) Cost ($) CPU time (s)
BCO
EP
PSO
RCGA
43.9457 98.5888 112.9320 209.7719 98.8000 44.0000 12.0974 78.0236 59.8790 8.0384 10317 5.1563
61.3610 95.1205 99.9427 208.7319 98.8000 44.0000 18.0713 77.5548 54.3739 7.9561 10390 5.2750
18.4626 124.2602 112.7794 209.8158 98.8140 44.0107 57.9236 32.7603 59.3161 8.1427 10613 5.3844
74.6834 97.9578 167.2308 124.9079 98.8008 44.0001 58.0965 32.4116 59.4919 7.5808 10667 6.4723
F c6 ðP6 ; H6 Þ ¼ 1250 þ 36P 6 þ 0:0435P26 þ 0:6H6 þ 0:027H26 þ 0:11P6 H6 $ to read as:
Table 2 Results obtained from proposed algorithm.
F c6 ðP6 ; H6 Þ ¼ 1250 þ 36P 6 þ 0:0435P26 þ 0:6H6 þ 0:027H26 þ 0:011P6 H6 $ According to the obtained active power transmission loss PL in Table 1, the matrix of network loss coefficients should be read as:
DOI of original article: http://dx.doi.org/10.1016/j.eswa.2011.03.067.
⇑ Corresponding author. Tel.: +98 21 73225612.
E-mail address: [email protected] (H.R. Abdolmohammadi). 0957-4174/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.eswa.2012.05.029
BD P1 (MW) P2 (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) H5 (MWth) H6 (MWth) H5 (MWth) PL (MW) Cost ($) CPU time (s)
52.7069 98.5398 112.6735 209.8158 93.8120 40.0000 29.3674 75.0000 45.6326 7.5480 10111 3.4584
13074
H.R. Abdolmohammadi, A. Kazemi / Expert Systems with Applications 39 (2012) 13073–13074
Table 3 Results obtained from BD, BCO, EP, PSO and RCGA (the bold number shows the changes from the Basu (2011)). BD (proposed algorithm)
BCO (Basu, 2011)
EP (Basu, 2011)
PSO (Basu, 2011)
RCGA (Basu, 2011)
PL (MW) Cost ($)
7.5480 10111
7.5447 10317
7.5594 10420
7.7046 10613
7.3310 10667
2
14 15 15 20 25
49 6 14 6 6 6 15 B¼6 6 15 6 6 4 20
3
45 16 20 18 19 7 7 7 16 39 10 12 15 7 7 106 20 10 40 14 11 7 7 7 18 12 14 35 17 5
it is obvious that the best performance is obtained by the proposed algorithm.
ðMW1 Þ
25 19 15 11 17 39 which is 10 times the network loss coefficients in Appendix A.3 of Basu (2011). In this comment, an algorithm based on Benders decomposition (BD) has been applied to a test system proposed by Basu (2011). Table 2 presents the solutions of the test system obtained using the proposed algorithm, and Table 3 compares them with the results reported by other methods. It can be observed in Table 3 that there is an error in the reported transmission loss PL in Table 1 and
2. Conclusions Several errors in the test system data and the solutions of CHPED problem in Basu (2011) have been pointed out. An efficient method based on Benders decomposition has been proposed for solving the problem. References Basu, M. (2011). Bee colony optimization for combined heat and power economic dispatch. Expert Systems with Applications, 38, 13527–13531. Guo, T., Henwood, M. I., & van Ooijen, M. (1996). An algorithm for heat and power dispatch. IEEE Transactions on Power Systems, 11(4), 1778–1784.
Contents lists available at SciVerse ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
Discussion
Comment on ‘‘Bee colony optimization for combined heat and power economic dispatch’’ by M. Basu [Expert Systems with Applications 38 (2011) 13527–13531] H.R. Abdolmohammadi ⇑, A. Kazemi Centre of Excellence for Power System Automation and Operation, Department of Electrical Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran
a r t i c l e
i n f o
Keywords: Cogeneration Combined heat and power economic dispatch Optimization
a b s t r a c t We comment on error in a recently published paper by M. Basu [Expert Systems with Applications 38 (2011) 13527–13531]. The optimization algorithm based on Benders decomposition has been applied to a test system and the results are compared with those of bee colony optimization, particle swarm optimization, real-coded genetic algorithm and evolutionary programing techniques. The numerical results demonstrate that the proposed method has more advantages than other methods in application. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Firstly, it must be stated that Basu presented an interesting algorithm for solving combined heat and power economic dispatch (CHPED) problems in Basu (2011). Unlike previous works on CHPED problems, which did not consider transmission loss, the above article considers the active power transmission loss. However, in the above-mentioned article, errors were found in the system data and the reported results. The cogeneration units and their cost functions were originally proposed by Guo et al. (1996). Therefore, in Appendix A.1 of Basu (2011), it is necessary for the cost function of sixth cogeneration unit:
Table 1 Results obtained from BCO, EP, PSO and RCGA (Table 1 of Basu (2011)).
P1 (MW) P2 (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) H5 (MWth) H6 (MWth) H5 (MWth) PL (MW) Cost ($) CPU time (s)
BCO
EP
PSO
RCGA
43.9457 98.5888 112.9320 209.7719 98.8000 44.0000 12.0974 78.0236 59.8790 8.0384 10317 5.1563
61.3610 95.1205 99.9427 208.7319 98.8000 44.0000 18.0713 77.5548 54.3739 7.9561 10390 5.2750
18.4626 124.2602 112.7794 209.8158 98.8140 44.0107 57.9236 32.7603 59.3161 8.1427 10613 5.3844
74.6834 97.9578 167.2308 124.9079 98.8008 44.0001 58.0965 32.4116 59.4919 7.5808 10667 6.4723
F c6 ðP6 ; H6 Þ ¼ 1250 þ 36P 6 þ 0:0435P26 þ 0:6H6 þ 0:027H26 þ 0:11P6 H6 $ to read as:
Table 2 Results obtained from proposed algorithm.
F c6 ðP6 ; H6 Þ ¼ 1250 þ 36P 6 þ 0:0435P26 þ 0:6H6 þ 0:027H26 þ 0:011P6 H6 $ According to the obtained active power transmission loss PL in Table 1, the matrix of network loss coefficients should be read as:
DOI of original article: http://dx.doi.org/10.1016/j.eswa.2011.03.067.
⇑ Corresponding author. Tel.: +98 21 73225612.
E-mail address: [email protected] (H.R. Abdolmohammadi). 0957-4174/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.eswa.2012.05.029
BD P1 (MW) P2 (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) H5 (MWth) H6 (MWth) H5 (MWth) PL (MW) Cost ($) CPU time (s)
52.7069 98.5398 112.6735 209.8158 93.8120 40.0000 29.3674 75.0000 45.6326 7.5480 10111 3.4584
13074
H.R. Abdolmohammadi, A. Kazemi / Expert Systems with Applications 39 (2012) 13073–13074
Table 3 Results obtained from BD, BCO, EP, PSO and RCGA (the bold number shows the changes from the Basu (2011)). BD (proposed algorithm)
BCO (Basu, 2011)
EP (Basu, 2011)
PSO (Basu, 2011)
RCGA (Basu, 2011)
PL (MW) Cost ($)
7.5480 10111
7.5447 10317
7.5594 10420
7.7046 10613
7.3310 10667
2
14 15 15 20 25
49 6 14 6 6 6 15 B¼6 6 15 6 6 4 20
3
45 16 20 18 19 7 7 7 16 39 10 12 15 7 7 106 20 10 40 14 11 7 7 7 18 12 14 35 17 5
it is obvious that the best performance is obtained by the proposed algorithm.
ðMW1 Þ
25 19 15 11 17 39 which is 10 times the network loss coefficients in Appendix A.3 of Basu (2011). In this comment, an algorithm based on Benders decomposition (BD) has been applied to a test system proposed by Basu (2011). Table 2 presents the solutions of the test system obtained using the proposed algorithm, and Table 3 compares them with the results reported by other methods. It can be observed in Table 3 that there is an error in the reported transmission loss PL in Table 1 and
2. Conclusions Several errors in the test system data and the solutions of CHPED problem in Basu (2011) have been pointed out. An efficient method based on Benders decomposition has been proposed for solving the problem. References Basu, M. (2011). Bee colony optimization for combined heat and power economic dispatch. Expert Systems with Applications, 38, 13527–13531. Guo, T., Henwood, M. I., & van Ooijen, M. (1996). An algorithm for heat and power dispatch. IEEE Transactions on Power Systems, 11(4), 1778–1784.