Economic Dispatch Using Modified Bat Algorithm
Abstract
:1. Introduction
2. Problem Formulation
2.1. Problem Objectives
2.2. Problem Constraints
3. Bat Algorithm
4. Modifications
4.1. Add Bad Experience Component
4.2. Nonlinear Inertia Weight
5. Experiments and Results
5.1. Test Case 1—Six-Generator Test System with System Losses
Generator | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
Pmin (MW) | 10 | 10 | 35 | 35 | 130 | 125 |
Pmax (MW) | 125 | 150 | 225 | 210 | 325 | 315 |
No. | a | b | c |
---|---|---|---|
1 | 0.15240 | 38.53973 | 756.79886 |
2 | 0.10587 | 46.15916 | 451.32513 |
3 | 0.02803 | 40.39655 | 1049.9977 |
4 | 0.03546 | 38.30553 | 1243.5311 |
5 | 0.02111 | 36.32782 | 1658.5596 |
6 | 0.01799 | 38.27041 | 1356.6592 |
Parameter | Value |
---|---|
0.9 | |
0.1 | |
[0.97 0.95] | |
[0.4 0.9] | |
2000 | |
[10 200] |
P1 (MW) | P2 (MW) | P3 (MW) | P4 (MW) | P5 (MW) | P6 (MW) | Loss (MW) | Cost ($/h) | ||
---|---|---|---|---|---|---|---|---|---|
λ Iteration | 28.304 | 10 | 118.897 | 118.733 | 230.733 | 212.831 | 19.433 | 36912.14 | |
GA | Best | 26.79976 | 15.89313 | 107.3073 | 123.932 | 228.3426 | 217.1609 | 19.44 | 36924.15 |
Avg. | 45.57365 | 48.619 | 105.8057 | 106.478 | 211.4508 | 200.6767 | 18.61 | 37505.72 | |
Std | 19.7706 | 28.6733 | 43.3288 | 36.2062 | 45.62 | 45.0436 | 1.325 | 382.88 | |
PSO | Best | 28.30223 | 9.999884 | 118.9522 | 118.6706 | 230.7563 | 212.7375 | 19.431 | 36911.54 |
Avg. | 28.39792 | 10.02338 | 119.0863 | 118.5947 | 230.588 | 212.7238 | 19.4262 | 36911.75 | |
Std | 0.85864 | 0.13943 | 0.83555 | 0.62292 | 1.1889 | 0.4948 | 0.027862 | 1.4869 | |
BA | Best | 28.07394 | 10.05693 | 119.9855 | 117.7729 | 231.1333 | 212.3918 | 19.4238 | 36911.79 |
Avg. | 28.39414 | 10.26771 | 119.159 | 119.0363 | 230.2951 | 212.2449 | 19.4092 | 36912.54 | |
Std | 0.69285 | 0.26761 | 2.2262 | 1.7091 | 2.9539 | 3.8 | 0.059993 | 1.0006 | |
MBA | Best | 28.14831 | 10.03893 | 119.7243 | 118.052 | 231.0219 | 212.4194 | 19.4239 | 36911.27 |
Avg. | 28.28837 | 10.21736 | 119.3942 | 118.6366 | 230.4744 | 212.3904 | 19.4146 | 36912.13 | |
Std | 0.73114 | 0.19558 | 2.485 | 1.8194 | 3.38 | 3.6097 | 0.065668 | 0.84625 |
P1 (MW) | P2 (MW) | P3 (MW) | P4 (MW) | P5 (MW) | P6 (MW) | Loss (MW) | Cost ($/h) | ||
---|---|---|---|---|---|---|---|---|---|
λ Iteration | 32.599 | 14.483 | 141.544 | 136.041 | 257.6588 | 243.003 | 25.330 | 41896.63 | |
GA | Best | 39.63015 | 13.23341 | 170.317 | 155.1286 | 232.4949 | 213.4204 | 24.2359 | 41976.08 |
Avg. | 55.35765 | 54.95395 | 130.4268 | 134.2949 | 230.3903 | 218.5409 | 23.9787 | 42614.68 | |
Std | 25.9155 | 30.1187 | 45.3717 | 39.9879 | 49.7911 | 45.6905 | 1.3105 | 436.61 | |
PSO | Best | 32.59937 | 14.48227 | 141.5412 | 136.0392 | 257.6555 | 242.9997 | 25.3299 | 41895.98 |
Avg. | 32.5959 | 14.51256 | 141.4859 | 135.9388 | 257.6442 | 243.1419 | 25.3322 | 41896.02 | |
Std | 0.19817 | 0.2575 | 0.31681 | 0.66662 | 0.33471 | 0.86126 | 0.020216 | 0.23259 | |
BA | Best | 32.46774 | 14.34427 | 141.9097 | 135.7294 | 257.7276 | 243.1421 | 25.3359 | 41895.88 |
Avg. | 32.58662 | 14.49149 | 141.7122 | 136.2057 | 257.3597 | 242.9548 | 25.3232 | 41896.17 | |
Std | 0.38275 | 0.49502 | 0.97076 | 0.88628 | 1.2144 | 1.3829 | 0.037035 | 0.25826 | |
MBA | Best | 32.49975 | 14.43056 | 141.6805 | 135.9817 | 257.502 | 243.2203 | 25.3329 | 41895.71 |
Avg. | 32.6766 | 14.35507 | 142.1353 | 135.802 | 257.5361 | 242.803 | 25.3222 | 41896.09 | |
Std | 0.12392 | 0.37326 | 0.61012 | 0.59674 | 0.31035 | 1.0403 | 0.03666 | 0.21975 |
5.2. Test Case 2–Five-Generator Test System with System Losses
Generator | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
Pmin (MW) | 50 | 20 | 30 | 10 | 40 |
Pmax (MW) | 300 | 125 | 175 | 75 | 250 |
No. | |||||
---|---|---|---|---|---|
1 | 0.0015 | 1.8 | 40 | 200 | 0.035 |
2 | 0.0030 | 1.8 | 60 | 140 | 0.040 |
3 | 0.0012 | 2.1 | 100 | 160 | 0.038 |
4 | 0.0080 | 2.0 | 25 | 100 | 0.042 |
5 | 0.0010 | 2.0 | 120 | 180 | 0.037 |
P1 (MW) | P2 (MW) | P3 (MW) | P4 (MW) | P5 (MW) | Cost ($/h) | ||
---|---|---|---|---|---|---|---|
GA | Best | 234.82 | 100.92 | 112.80 | 71.46 | 209.99 | 2068.06 |
Avg. | 253.89 | 91.39 | 127.71 | 49.37 | 207.62 | 2357.02 | |
Std | 29.12 | 19.19 | 27.23 | 15.85 | 23.30 | 111.80 | |
PSO | Best | 229.51 | 102.98 | 112.67 | 75.00 | 209.81 | 2029.63 |
Avg. | 248.71 | 94.28 | 126.39 | 55.04 | 205.56 | 2165.08 | |
Std | 30.85 | 19.33 | 27.77 | 23.06 | 26.58 | 104.24 | |
BA | Best | 229.14 | 101.30 | 114.05 | 74.26 | 211.23 | 2042.88 |
Avg. | 250.69 | 90.03 | 133.26 | 53.18 | 202.84 | 2176.06 | |
Std | 38.69 | 26.89 | 32.47 | 27.81 | 28.00 | 106.92 | |
MBA | Best | 231.06 | 99.59 | 113.48 | 74.42 | 211.44 | 2032.23 |
Avg. | 256.94 | 96.53 | 131.55 | 47.81 | 197.14 | 2141.50 | |
Std | 35.60 | 17.06 | 29.09 | 29.65 | 30.24 | 95.39 |
6. Conclusions
Author Contributions
Conflicts of Interest
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Latif, A.; Palensky, P. Economic Dispatch Using Modified Bat Algorithm. Algorithms 2014, 7, 328-338. https://doi.org/10.3390/a7030328
Latif A, Palensky P. Economic Dispatch Using Modified Bat Algorithm. Algorithms. 2014; 7(3):328-338. https://doi.org/10.3390/a7030328
Chicago/Turabian StyleLatif, Aadil, and Peter Palensky. 2014. "Economic Dispatch Using Modified Bat Algorithm" Algorithms 7, no. 3: 328-338. https://doi.org/10.3390/a7030328