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Table 17 Simulation results for TSys-3 (15-unit system)

From: An advanced hybrid meta-heuristic algorithm for solving small- and large-scale engineering design optimization problems

Power output (MW) Compared algorithms Proposed algorithms
PSO GA MTVPSO EHM BCO NCS MPSO-TVAC θ-PSO DEPSO DPD aDE aPSO haDEPSO
1 455.00 415.3108 454.9812 455 452.9151 455.00 455.00 455 455 454.9999 454.8834 454.8823 454.9813
2 380.00 359.7206 455 380 358.8547 380.00 380.00 380 420 454.9999 455.0000 455.0000 455.0000
3 130.00 104.4250 130 130 127.6452 130.00 130.00 130 130 130.0000 130.0000 130.0000 130.0000
4 130.00 74.9853 130 130 128.4156 130.00 130.00 130 130 130.0000 130.0000 130.0000 130.0000
5 154.42 380.2844 235.5844 170 276.0158 170.00 170.00 170 270 234.2005 239.1899 240.9334 239.4334
6 460.00 426.7902 460 460 429.9371 460.00 459.99 460 460 460.0000 460.0000 460.0000 460.0000
7 430.00 341.3164 465 430 437.8152 430.00 430.00 430 430 464.9999 462.0000 460.0000 460.0000
8 60.00 124.7867 60 90.14947 62.8458 60.00 72.60 75.0139 60 60.00000 61.0000 60.0000 60.0000
9 74.27 133.1445 25 37.75777 59.5343 71.05 58.32 55.8293 25 25.00000 24.0000 26.0000 25.0000
10 160.00 89.2567 28.9867 160 96.7215 159.85 159.73 160 62 30.99387 28.6810 28.9997 28.8757
11 80.00 60.0572 76.8357 80 75.2118 80.00 80.00 80 80 76.70138 75.9970 76.1987 75.1865
12 79.60 49.9998 80 80 78.4522 80.00 80.00 80 80 79.99999 80.0000 80.0000 80.0000
13 25.00 38.7713 25 25 35.5118 25 25.01 25.0012 25 25.00000 26.0000 25.0000 25.0000
14 27.59 41.9425 15 15 19.1549 15 15.00 15.0000 15 15.00000 15.0000 15.0000 15.0000
15 15.00 22.6445 15 15 21.0143 15 15.00 15.0181 15 15.00000 15.0000 15.0000 15.0000
Total power (MW) 2660.88 2630.0 2656.3882 2657.90724 2660.0483 2660.9 2660.66 2660.8625 2657.96 2656.89544 2656.7513 2657.0141 2653.4769
Power loss (MW) 30.88 38.2782 26.3882 27.90724 29.4073 30.908 30.66 30.8699 27.976 26.89544 26.7513 27.0141 23.4769
Power balance (MW) 0.00000 0.1218 0.00000 0.0 0.641 0.0 0.00000 − 0.0074 0.010 0.00000 0.00000 0.00000 0.00000
Min cost ($/h) 32,731.96 33,113 32,542.7320 32,672.9595 32,714.265 32,708 32,704.47 32,706.6048 32,588.81 32,548.5857 32,542.7820 32,542.4512 32,542.1452
Mean cost ($/h) 33,039.00 33,254 32,550.9885 32,699.2548 32,725.251 32,854 32,705.00 32,709.3196 32,591.49 32,556.6793 32,550.9055 32,550.5421 32,550.7457
Max cost ($/h) 33,331.00 33,285 32,562.4861 32,708.8547 32,755.369 32,975 32,728.99 32,739.4865 32,588.99 32,564.4051 32,562.4814 32,559.2411 32,558.2584
Std. of cost ($/h) 2.8475 1.598 2.04619 3.5841 2.4584 6.2541 3.51 7.3140 4.02 2.095632 1.85214 1.97548 1.04350
CPU mean time (s) 26.59 49.31 0.190 0.368 12.42 12.79 12.78 11.7380 1.96 1.98594 0.175 0.172 0.181