Journal of Electrical Engineering ›› 2020, Vol. 15 ›› Issue (3): 1-12.doi: 10.11985/2020.03.001
LI Xiaozhu(
),WANG Weiqing()
Received:2020-04-16
Revised:2020-07-09
Online:2020-09-25
Published:2020-10-28
CLC Number:
LI Xiaozhu,WANG Weiqing. Dynamic Environmental Economic Dispatch of Wind Farm Based on Multi-objective Moth-flame Optimization[J]. Journal of Electrical Engineering, 2020, 15(3): 1-12.
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| MOMFO | MOSADDE | NSGA-Ⅱ | SPGA2 | MOPSO | |
|---|---|---|---|---|---|
| NP | 100 | 100 | 100 | 100 | 100 |
| Amax | 100 | 100 | 100 | 100 | 100 |
| flame.max | 100 | — | — | — | — |
| 变尺度收缩因子β | 1 | — | — | — | — |
| 交叉分布指数ηc | — | — | 20 | 20 | — |
| 变异分布指数ηm | — | — | 20 | 20 | — |
| 交叉概率Pc | — | [0.1, 0.9] | 0.9 | 0.9 | — |
| 变异概率Pm | — | [0, 0.5] | 1/d | 1/d | — |
| 变异率 | — | — | — | — | 0.5 |
| 自适应网格维数 | — | — | — | — | 250 |
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| 函数名 | MOMFO(GD) | MOSADDE(GD) | NSGA-Ⅱ(GD) | SPEA2(GD) | MOPSO(GD) | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| X-z | IQR | X-z | IQR | X-z | IQR | X-z | IQR | X-z | IQR | |
| Fonseca | 2.799×10-4 | 3.874×10-5 | 1.479×10-4 | 1.1×10-5 | 3.116×10-4 | 4.1×10-5 | 2.281×10-4 | 2.6×10-5 | 3.274×10-4 | 5.6×10-4 |
| Schaffer | 1.829×10-5 | 1.266×10-6 | 2.356×10-4 | 1.8×10-5 | 2.465×10-4 | 4.9×10-5 | 2.752×10-4 | 9.0×10-5 | 2.443×100 | 5.4×10-4 |
| ZDT1 | 1.017×10-4 | 8.620×10-5 | 1.645×10-4 | 6.9×10-5 | 2.196×10-4 | 6.6×10-5 | 1.575×10-3 | 2.1×10-2 | 1.692×10-2 | 1.1×10-2 |
| ZDT2 | 9.779×10-5 | 1.282×10-5 | 5.396×10-5 | 9.6×10-6 | 1.687×10-4 | 4.6×10-5 | 4.995×10-3 | 5.4×10-3 | 5.298×10-2 | 4.1×10-2 |
| ZDT3 | 1.747×10-4 | 1.754×10-5 | 3.110×10-4 | 4.1×10-5 | 3.532×10-4 | 1.3×10-5 | 1.701×10-3 | 4.2×10-3 | 4.869×10-2 | 9.0×10-3 |
| ZDT4 | 1.041×10-5 | 3.340×10-6 | 1.027×10-4 | 6.7×10-5 | 5.185×10-4 | 1.4×10-4 | 1.128×10-1 | 6.5×10-3 | 2.097×10-1 | 2.5×10-1 |
| ZDT6 | 2.201×10-2 | 3.863×10-2 | 4.176×10-4 | 1.5×10-5 | 7.943×10-3 | 1.1×10-3 | 1.915×10-3 | 1.6×10-4 | 1.992×10-2 | 5.3×10-2 |
| DTLZ2 | 2.081×10-3 | 5.721×10-4 | 5.901×10-4 | 3.3×10-5 | 1.243×10-3 | 2.2×10-4 | 5.183×10-3 | 3.2×10-3 | 1.319×10-2 | 6.3×10-3 |
| DTLZ3 | 1.098×10-3 | 9.370×10-5 | 7.368×10-4 | 3.7×10-5 | 4.692×10-3 | 1.6×10-2 | 6.092×10-2 | 9.8×10-2 | 3.652×101 | 5.4×101 |
| DTLZ4 | 6.923×10-3 | 1.019×10-3 | 5.364×10-4 | 4.2×10-5 | 1.200×10-3 | 4.1×10-4 | 3.489×10-3 | 3.9×10-3 | 1.063×10-2 | 3.6×10-3 |
| 函数名 | MOMFO(Δ) | MOSADDE(Δ) | NSGA-Ⅱ(Δ) | SPEA2(Δ) | MOPSO(Δ) | |||||
| X-z | IQR | X-z | IQR | X-z | IQR | X-z | IQR | X-z | IQR | |
| Fonseca | 1.344×10-3 | 2.296×10-4 | 1.156×10-1 | 1.1×10-2 | 3.769×10-1 | 3.1×10-2 | 1.788×10-1 | 1.3×10-2 | 7.781×10-1 | 3.4×10-1 |
| Schaffer | 2.480×10-3 | 3.496×10-4 | 1.408×10-1 | 1.6×10-2 | 2.862×10-1 | 2.5×10-2 | 2.741×10-1 | 2.4×10-2 | 7.373×10-4 | 5.3×10-2 |
| ZDT1 | 5.346×10-4 | 5.346×10-4 | 1.325×10-1 | 6.7×10-3 | 5.077×10-1 | 3.0×10-2 | 2.676×10-1 | 1.8×10-1 | 2.949×10-1 | 2.7×10-2 |
| ZDT2 | 5.403×10-4 | 1.193×10-4 | 1.256×10-1 | 1.5×10-2 | 4.831×10-1 | 2.3×10-2 | 4.322×10-1 | 3.2×10-1 | 2.851×10-1 | 1.6×10-2 |
| ZDT3 | 6.968×10-4 | 6.898×10-5 | 4.627×10-1 | 8.8×10-3 | 5.881×10-1 | 4.8×10-2 | 4.754×10-1 | 6.0×10-2 | 6.150×10-1 | 4.1×10-3 |
| ZDT4 | 5.407×10-4 | 9.785×10-5 | 1.169×10-1 | 1.0×10-2 | 3.373×10-1 | 2.3×10-2 | 6.678×10-1 | 6.8×10-1 | 3.145×10-1 | 5.2×10-2 |
| ZDT6 | 5.095×10-4 | 1.734×10-2 | 1.332×10-1 | 1.4×10-2 | 4.946×10-1 | 4.4×10-2 | 2.363×10-1 | 2.8×10-1 | 1.156×100 | 1.3×10-1 |
| DTLZ2 | 2.029×10-3 | 3.026×10-4 | 6.034×10-1 | 5.0×10-2 | 8.246×10-1 | 8.7×10-2 | 2.413×10-1 | 5.4×10-2 | 7.868×10-1 | 4.0×10-1 |
| DTLZ3 | 7.656×10-3 | 1.467×10-3 | 5.870×10-1 | 4.3×10-2 | 8.879×10-1 | 7.3×10-2 | 2.188×10-1 | 5.0×10-2 | — | — |
| DTLZ4 | 4.183×10-3 | 6.659×10-4 | 1.594×100 | 3.6×10-1 | 7.749×10-1 | 8.3×10-2 | 2.413×10-1 | 5.6×10-2 | 1.594×100 | 3.7×10-1 |
| 函数名 | MOMFO(HVR) | MOSADDE(HVR) | NSGA-Ⅱ(HVR) | SPEA2(HVR) | MOPSO(HVR) | |||||
| X-z | IQR | X-z | IQR | X-z | IQR | X-z | IQR | X-z | IQR | |
| Fonseca | 9.999×10-1 | 2.745×10-6 | 9.980×10-1 | 3.8×10-4 | 9.798×102 | 1.0×10-3 | 9.853×10-1 | 9.4×10-4 | 9.641×10-1 | 3.9×10-2 |
| Schaffer | 9.989×10-1 | 5.645×10-5 | 9.973×10-1 | 5.0×10-5 | 9.969×10-1 | 1.3×10-5 | 9.968×10-1 | 1.9×10-4 | 9.967×10-1 | 1.1×10-3 |
| ZDT1 | 9.999×10-1 | 2.924×10-6 | 9.971×10-1 | 4.6×10-4 | 9.947×10-1 | 3.2×10-4 | 9.914×10-1 | 9.3×10-4 | 9.423×10-1 | 9.4×10-2 |
| ZDT2 | 9.999×10-1 | 5.983×10-6 | 9.951×10-1 | 7.0×10-4 | 9.955×10-1 | 2.4×10-4 | 9.877×10-1 | 4.1×10-3 | 5.616×10-1 | 3.1×10-1 |
| ZDT3 | 9.985×10-1 | 2.557×10-5 | 9.979×10-1 | 3.1×10-4 | 9.971×10-1 | 3.0×10-4 | 9.863×10-1 | 4.6×10-3 | 6.278×10-1 | 6.4×10-2 |
| ZDT4 | 9.999×10-1 | 6.638×10-6 | 9.995×10-1 | 1.0×10-5 | 9.895×10-1 | 1.4×10-3 | 6.212×10-1 | 2.3×10-1 | 6.879×10-1 | 3.3×10-1 |
| ZDT6 | 8.462×10-1 | 1.414×10-4 | 9.994×10-1 | 4.0×10-5 | 8.667×10-1 | 1.8×10-2 | 9.389×10-1 | 7.2×10-3 | 9.496×10-1 | 3.0×10-3 |
| DTLZ2 | 9.798×10-1 | 1.277×10-5 | 9.790×10-1 | 2.4×10-3 | 9.591×10-1 | 1.5×10-3 | 9.961×10-1 | 6.4×10-4 | 9.858×10-1 | 8.0×10-3 |
| DTLZ3 | 9.395×10-1 | 5.940×10-5 | 9.790×10-1 | 1.5×10-3 | 9.277×10-1 | 1.7×10-1 | 8.610×10-1 | 1.6×10-1 | 0 | 0 |
| DTLZ4 | 9.695×10-1 | 4.628×10-5 | 9.794×10-1 | 3.6×10-3 | 9.692×10-1 | 6.5×10-1 | 9.598×10-1 | 6.6×10-2 | 9.319×10-1 | 1.5×10-2 |
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| 时段 | 出力/MW | 总出力/MW | 总负荷/MW | 网损/MW | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 机组1 | 机组2 | 机组3 | 机组4 | 机组5 | 机组6 | 机组7 | 机组8 | 机组9 | 机组10 | ||||
| 1 | 208.286 8 | 153.743 4 | 87.938 8 | 134.521 7 | 132.493 3 | 96.132 5 | 81.952 2 | 81.232 3 | 67.518 5 | 12.517 8 | 1 056.33 | 1 036 | 20.337 1 |
| 2 | 158.308 2 | 141.352 1 | 121.862 5 | 139.941 3 | 154.051 5 | 82.707 3 | 111.847 2 | 100.120 8 | 80.000 0 | 42.425 0 | 1 132.61 | 1 110 | 22.616 0 |
| 3 | 150.000 0 | 210.568 7 | 174.641 3 | 136.440 3 | 201.879 9 | 130.957 5 | 81.847 2 | 90.261 9 | 69.169 1 | 41.490 2 | 1 287.25 | 1 258 | 29.256 0 |
| 4 | 202.147 6 | 203.093 1 | 185.083 1 | 129.684 9 | 205.761 0 | 180.957 5 | 104.266 5 | 115.417 0 | 76.665 5 | 39.547 0 | 1 442.62 | 1 406 | 36.623 3 |
| 5 | 204.120 2 | 211.292 3 | 177.730 8 | 168.183 3 | 212.870 7 | 218.220 1 | 107.329 1 | 96.460 7 | 71.577 3 | 52.667 5 | 1 520.45 | 1 480 | 40.452 0 |
| 6 | 242.281 6 | 225.952 1 | 193.957 0 | 191.885 3 | 230.372 3 | 251.676 7 | 122.802 8 | 109.057 7 | 72.393 3 | 36.880 2 | 1 677.25 | 1 628 | 49.258 9 |
| 7 | 249.314 8 | 261.332 6 | 240.759 6 | 203.914 4 | 206.650 5 | 221.066 7 | 130.000 0 | 120.000 0 | 79.794 5 | 43.465 4 | 1 756.29 | 1 702 | 54.298 4 |
| 8 | 205.251 9 | 257.850 1 | 292.158 2 | 216.883 8 | 243.000 0 | 245.915 8 | 127.527 8 | 114.445 0 | 76.408 1 | 55.000 0 | 1 834.44 | 1 776 | 58.440 6 |
| 9 | 273.392 1 | 289.902 6 | 291.120 4 | 265.840 9 | 242.209 0 | 252.426 1 | 128.152 5 | 119.342 9 | 79.692 8 | 51.716 4 | 1 993.79 | 1 924 | 69.795 6 |
| 10 | 297.351 7 | 326.621 7 | 326.873 9 | 280.490 0 | 240.583 4 | 256.049 7 | 127.997 7 | 117.747 2 | 77.690 3 | 48.607 7 | 2 100.01 | 2 022 | 78.013 3 |
| 11 | 324.446 9 | 362.693 7 | 336.622 3 | 292.714 7 | 239.710 2 | 259.848 5 | 128.340 8 | 120.000 0 | 76.897 4 | 50.348 4 | 2 191.62 | 2 106 | 85.623 0 |
| 12 | 337.018 8 | 388.646 7 | 335.529 1 | 297.798 2 | 241.606 5 | 258.649 5 | 129.115 1 | 118.806 2 | 77.805 4 | 54.920 3 | 2 239.89 | 2 150 | 89.895 8 |
| 13 | 314.804 4 | 356.536 9 | 315.310 4 | 300.000 0 | 237.991 3 | 258.068 1 | 125.526 4 | 115.625 6 | 78.989 1 | 51.802 9 | 2 154.65 | 2 072 | 82.655 1 |
| 14 | 290.264 7 | 292.614 3 | 312.749 9 | 263.373 4 | 230.910 3 | 232.307 0 | 124.392 1 | 120.000 0 | 72.664 6 | 55.000 0 | 1 994.27 | 1 924 | 70.276 3 |
| 15 | 236.030 4 | 226.984 1 | 232.749 9 | 269.343 2 | 234.058 4 | 259.051 3 | 128.134 0 | 115.109 4 | 79.373 3 | 53.473 0 | 1 834.30 | 1 776 | 58.306 9 |
| 16 | 166.587 2 | 186.486 1 | 254.160 6 | 221.811 3 | 202.780 7 | 228.322 1 | 128.986 0 | 86.178 1 | 67.490 1 | 55.000 0 | 1 597.80 | 1 554 | 43.802 2 |
| 17 | 160.794 0 | 155.264 0 | 189.395 3 | 219.133 3 | 225.296 7 | 236.951 6 | 117.280 3 | 107.968 3 | 67.651 9 | 39.584 1 | 1 519.31 | 1 480 | 39.319 3 |
| 18 | 185.509 8 | 220.097 2 | 242.625 0 | 181.025 0 | 239.579 5 | 238.586 8 | 128.060 9 | 119.504 3 | 67.973 3 | 53.585 0 | 1 676.54 | 1 628 | 48.546 8 |
| 19 | 226.825 6 | 219.634 9 | 269.395 3 | 240.652 4 | 243.000 0 | 258.404 0 | 121.705 3 | 119.539 6 | 80.000 0 | 55.000 0 | 1 834.15 | 1 776 | 58.157 1 |
| 20 | 268.653 0 | 290.801 8 | 322.391 6 | 280.889 2 | 243.000 0 | 259.866 1 | 129.481 2 | 120.000 0 | 79.656 2 | 50.499 3 | 2 045.23 | 1 972 | 73.238 4 |
| 21 | 274.061 5 | 295.313 7 | 289.334 4 | 276.912 1 | 240.496 6 | 238.722 9 | 130.000 0 | 120.000 0 | 78.322 1 | 50.747 1 | 1 993.91 | 1 924 | 69.910 5 |
| 22 | 206.320 0 | 218.698 8 | 249.080 5 | 228.133 8 | 220.951 5 | 208.404 0 | 125.707 8 | 109.269 8 | 64.573 0 | 45.614 3 | 1 676.75 | 1 628 | 48.753 4 |
| 23 | 158.849 2 | 140.637 7 | 177.216 8 | 197.530 7 | 192.812 9 | 202.698 9 | 96.557 1 | 95.989 1 | 73.134 5 | 28.419 1 | 1 363.84 | 1 332 | 31.846 0 |
| 24 | 153.472 1 | 141.078 8 | 169.994 9 | 178.708 7 | 173.569 3 | 162.371 3 | 96.229 0 | 79.572 2 | 38.285 9 | 15.930 1 | 1 209.21 | 1 184 | 25.212 4 |
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| MOMFO | Pro_ NSGA-Ⅱ | MAMODE | IBFA | EMOD EDCH | Pro _PSO | Pro_ MOEA/D | IMOEA/D_ CH | RCGA/ NSGA-Ⅱ | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 燃料成本/€ | 2 488 134.68 | 2 555 180.88 | 2 514 113 | 2 517 117 | 2 530 558.94 | 2 508 637.51 | 2 516 800.658 | 2 514 600 | 2 522 600 | ||
| 污染排放/1b | 286 009.59 | 299 140.86 | 302 742 | 299 037 | 299 124.96 | 296 807.30 | 297 015.14 | 298 360 | 309 940 | ||
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| 时段 | 出力/MW | 总出力/MW | 风电场预测/MW | 网损/MW | 总负荷/MW | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 机组1 | 机组2 | 机组3 | 机组4 | 机组5 | 机组6 | 机组7 | 机组8 | 机组9 | 机组10 | |||||
| 1 | 159.77 | 156.31 | 73.00 | 86.21 | 144.76 | 84.19 | 96.39 | 69.94 | 76.31 | 52.23 | 999.11 | 55 | 1 036 | 1 036 |
| 2 | 166.11 | 163.57 | 124.17 | 127.80 | 106.45 | 128.80 | 81.44 | 89.29 | 64.00 | 29.10 | 1 080.74 | 50 | 1 110 | 1 110 |
| 3 | 155.80 | 180.54 | 163.25 | 145.95 | 136.04 | 125.16 | 111.22 | 97.45 | 74.60 | 29.05 | 1 219.06 | 65 | 1 258 | 1 258 |
| 4 | 191.84 | 213.45 | 205.74 | 137.22 | 157.75 | 148.70 | 101.93 | 118.03 | 74.89 | 42.77 | 1 392.31 | 48 | 1 406 | 1 406 |
| 5 | 203.50 | 185.94 | 188.93 | 183.34 | 207.52 | 194.52 | 97.62 | 120.00 | 47.94 | 50.85 | 1 480.17 | 38 | 1 480 | 1 480 |
| 6 | 219.98 | 225.84 | 208.06 | 183.17 | 241.62 | 196.20 | 116.57 | 113.72 | 73.69 | 47.46 | 1 626.32 | 48 | 1 628 | 1 628 |
| 7 | 221.73 | 232.39 | 202.17 | 196.55 | 242.79 | 246.20 | 128.69 | 114.19 | 66.25 | 46.20 | 1 697.16 | 55 | 1 702 | 1 702 |
| 8 | 220.18 | 223.40 | 227.27 | 234.50 | 243.00 | 255.99 | 129.08 | 117.21 | 77.36 | 55.00 | 1 782.98 | 48 | 1 776 | 1 776 |
| 9 | 260.13 | 225.48 | 306.06 | 284.23 | 241.49 | 259.98 | 126.18 | 120.00 | 80.00 | 55.00 | 1 958.56 | 32 | 1 924 | 1 924 |
| 10 | 272.68 | 303.52 | 334.46 | 283.81 | 241.78 | 259.26 | 130.00 | 120.00 | 78.12 | 54.13 | 2 077.76 | 20 | 2 022 | 2 022 |
| 11 | 337.93 | 326.11 | 318.08 | 295.70 | 242.36 | 258.08 | 128.87 | 111.83 | 77.98 | 51.20 | 2 148.12 | 40 | 2 106 | 2 106 |
| 12 | 324.28 | 356.08 | 339.46 | 299.72 | 233.27 | 258.32 | 119.64 | 119.80 | 79.75 | 54.82 | 2 185.13 | 50 | 2 150 | 2 150 |
| 13 | 274.72 | 316.03 | 327.42 | 287.80 | 241.41 | 260.00 | 123.99 | 119.89 | 78.78 | 53.32 | 2 083.35 | 65 | 2 072 | 2 072 |
| 14 | 275.85 | 236.03 | 254.63 | 296.80 | 234.16 | 255.09 | 127.11 | 111.14 | 71.94 | 53.37 | 1 916.13 | 72 | 1 924 | 1 924 |
| 15 | 229.78 | 231.97 | 208.24 | 258.17 | 230.67 | 248.22 | 104.12 | 115.24 | 64.99 | 47.26 | 1 738.67 | 90 | 1 776 | 1 776 |
| 16 | 150.00 | 225.98 | 218.69 | 208.17 | 184.75 | 198.22 | 84.65 | 108.56 | 77.56 | 36.11 | 1 492.69 | 100 | 1 554 | 1 554 |
| 17 | 150.43 | 257.12 | 150.07 | 158.17 | 186.52 | 183.19 | 111.20 | 117.64 | 78.16 | 38.53 | 1 431.04 | 85 | 1 480 | 1 480 |
| 18 | 162.54 | 234.03 | 216.09 | 169.09 | 227.85 | 224.43 | 125.67 | 116.72 | 77.17 | 50.98 | 1 604.57 | 68 | 1 628 | 1 628 |
| 19 | 201.36 | 233.64 | 250.41 | 212.46 | 238.81 | 260.00 | 123.24 | 115.76 | 80.00 | 54.49 | 1 770.17 | 60 | 1 776 | 1 776 |
| 20 | 275.34 | 284.26 | 276.34 | 248.97 | 241.47 | 259.38 | 130.00 | 120.00 | 79.40 | 55.00 | 1 970.16 | 70 | 1 972 | 1 972 |
| 21 | 289.26 | 257.48 | 271.54 | 228.49 | 236.81 | 248.64 | 128.68 | 117.55 | 80.00 | 55.00 | 1 913.45 | 75 | 1 924 | 1 924 |
| 22 | 209.77 | 177.65 | 266.70 | 178.57 | 204.47 | 235.03 | 98.88 | 120.00 | 50.20 | 40.11 | 1 581.38 | 90 | 1 628 | 1 628 |
| 23 | 161.2 | 135.00 | 198.44 | 184.01 | 164.46 | 209.04 | 68.88 | 90.00 | 48.11 | 21.08 | 1 280.24 | 80 | 1 332 | 1 332 |
| 24 | 150.24 | 135.04 | 187.62 | 129.58 | 154.47 | 185.03 | 68.88 | 90.00 | 20.22 | 10.12 | 1 131.21 | 75 | 1 184 | 1 184 |
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| MOMFO | IMOEA/D-CH | ||
|---|---|---|---|
| Case1 | Case2 | ||
| 燃料成本/€ | 2 488 134.68 | 2 380 716.51 | 2 387 000 |
| 污染排放/1b | 286 009.59 | 261 538.47 | 269 570 |
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| 风电场规模/倍 | 燃料成本/€ | 污染排放/1b | 总穿透功率(%) |
|---|---|---|---|
| 1.0 | 2 488 134.680 | 286 009.590 0 | 17.100 |
| 1.5 | 2 319 746.143 | 250 639.506 1 | 25.996 |
| 2.0 | 2 276 171.277 | 240 500.100 0 | 35.935 |
| 2.5 | — | — | — |
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