Optimal Scheduling of Hydro–Thermal–Wind–Photovoltaic Generation Using Lightning Attachment Procedure Optimizer
Abstract
:1. Introduction
Reference | Method | Year | Test System | Main Consideration |
---|---|---|---|---|
[26] | ALO | 2016 | Test System 1, Test System 3, Test System 5 | Valve-point loading effect (VPE), transmission loss. |
[5] | RCGA-RTVM | 2014 | Test System 1 | Valve-point loading effect of thermal units, power transmission loss. |
[27] | HMOCA incorporated DE | 2011 | Test System 1 | Minimization of emission issues. |
[19] | Multi-objective hybrid grey wolf optimizer | 2018 | Test System 2 | Minimization of operational costs and pollution emissions |
[28] | Fast convergence real-coded genetic algorithm | 2018 | Test System 2 | The effect of valve-point loading of thermal generator and transmission loss is taken into consideration |
[10] | IHS | 2018 | Test System 1 | Valve-point loading effect of thermal units, power transmission loss of the system. |
[29] | Improved DE | 2014 | Test System 1 | Prohibited discharge zones (PDZs) of hydro units, valve-point loading effect, ramp rate limits of thermal generators, transmission losses. |
[30] | CPSO | 2019 | Test System 1 | Valve-point loading effect, prohibited discharge zones (PDZs) of hydro units. |
[31] | MOABC | 2014 | Test System 1 | Valve-point loading effect, power transmission losses. |
[32] | NSGSA-CM | 2014 | Test System1 | Emission of hydrothermal system. |
[8] | TLBO | 2013 | Test System 1 | Valve-point effect of thermal plants, prohibited discharge zones (PDZs) of the water reservoir of the hydro units. |
[33] | A hybrid CSA and PSO | 2013 | Test System 1 | Economic emission, power transmission loss, valve-point effect. |
[34] | EP | 2004 | Test System 1 | Valve-point loading effect. |
[11] | MDNLPSO | 2015 | Test System 1 | Prohibited discharge zones (PDZs) of the water reservoir of the hydro units, valve-point loading effect, transmission losses. |
[35] | RCGA-AFSA | 2014 | Test System 1 | Valve-point loading effect, transmission losses, prohibited discharge zones (PDZs), ramp rate limits. |
[36] | TLPSOS | 2017 | Test System 1 | Valve-point loading effect. |
- The hydro–thermal generation scheduling problem is solved for small and large test systems.
- The renewable energy resources including the wind and PV generation systems are considered in the STHS problem.
- The economic issues are considered with cost reduction in the STHS problem.
- Application of efficient optimizer called LAPO to solve the STHS problem with renewable energy resources.
2. Problem Formulation of Hydrothermal Generation Scheduling with Wind and PV Power Integration System
2.1. The Cost Minimization
2.2. The Emission Rate Minimization
2.3. Constraints
2.4. Modeling of Wind and PV Power Generation
3. Lightning Attachment Procedure Optimization (LAPO)
Mathematical Model of LAPO
- Step 1: Trail spots
- Step 2: The next jumping of the initial points
- Step 3: Branch fading
- Step 4: Upward leader movement
- Step 5: The strike point
4. Simulation Results and Discussion
4.1. Test System 1
4.2. Test System 2
4.3. Test System 3
4.4. Test System 4
4.5. Test System 5
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Total cost of thermal, wind, and PV-generating units | |
Total cost of thermal-generating units | |
Total cost of wind-generating units | |
Total cost of PV-generating units. | |
Total number of thermal-generating units | |
Total number of wind-generating units | |
Total number of PV-generating units | |
T | length of total scheduling period |
Power generation from thermal unit at time t | |
Power generation from wind unit at time t | |
Power generation from PV unit at time t | |
,, | Fuel cost coefficients of thermal unit |
Minimum power generation limit of thermal unit | |
, | Valve-point impact coefficients of thermal unit |
Total amount of emission from all thermal units | |
, , , , | Emission coefficients of the thermal units |
Total number of hydropower-generating units | |
Power load demand of the system at time t | |
Power output of hydropower unit at time t | |
Power losses of the hydrothermal system at time t | |
, , , , | Power generation coefficients of hydropower unit |
Reservoir storage volume of hydropower unit at time t | |
Water discharge rate of hydropower unit at time t | |
Power transmission loss of the system at time t | |
Coefficients of power transmission loss | |
External inflow to reservoir at time t | |
Spillage discharge rate of reservoir at time t | |
Number of upstream hydropower unit | |
Minimum storage volume of hydropower unit | |
Maximum storage volume of hydropower unit | |
Minimum water discharge of hydropower unit | |
Maximum water discharge of hydropower unit | |
Minimum and maximum power generation of hydropower unit | |
Minimum and maximum power generation of thermal unit | |
Direct cost coefficient for wind power | |
Rated power of wind-generating unit | |
Cut in wind speed | |
Cut out wind speed | |
Rated wind speed | |
Direct cost coefficient for PV power | |
G | Forecast solar radiation |
Solar radiation in the standard environment | |
A certain radiation point | |
Equivalent rated power output of the PV unit |
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Test System | Number of Hydrothermal Generation Units |
---|---|
Test System 1 | Four cascaded hydropower plants and three thermal plants |
Test System 2 | Four cascaded hydropower plants, three thermal plants, and one equivalent wind-and-solar-generating unit |
Test System 3 | Four hydro plants and ten thermal plants |
Test System 4 | Four cascaded hydropower plants, eight thermal-power plants, and one equivalent wind- and equivalent solar-generating unit |
Test System 5 | Four cascaded hydropower plants, eight thermal-power plants, and two wind-generating units |
Hours (h) | Hydro Power (MW) | Thermal Power (MW) | Total Load (MW) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Qh1 | Qh2 | Qh3 | Qh4 | Ph1 | Ph2 | Ph3 | Ph4 | Ps1 | Ps2 | Ps3 | PD | |
1 | 11.881 | 14.880 | 17.128 | 10.441 | 92.37 | 83.227 | 29.169 | 177.984 | 102.638 | 124.877 | 139.724 | 750 |
2 | 5.299 | 6.082 | 22.175 | 17.215 | 55.483 | 46.549 | 4.485 | 216.396 | 102.675 | 124.887 | 229.522 | 780 |
3 | 13.802 | 13.592 | 11.488 | 23.312 | 95.463 | 78.521 | 38.674 | 207.574 | 20.012 | 209.757 | 50.007 | 700 |
4 | 14.552 | 14.352 | 27.639 | 24.236 | 91.949 | 75.821 | 0 | 199.121 | 102.669 | 40.001 | 139.801 | 650 |
5 | 5.8224 | 14.9813 | 25.821 | 15.967 | 56.246 | 72.473 | 0 | 258.852 | 102.664 | 40.0032 | 139.766 | 670 |
6 | 14.999 | 13.753 | 10.080 | 24.148 | 87.053 | 70.288 | 38.070 | 325.225 | 99.596 | 40 | 139.778 | 800 |
7 | 14.061 | 14.363 | 22.972 | 24.989 | 86.437 | 71.486 | 0 | 327.820 | 20.148 | 124.834 | 319.271 | 950 |
8 | 13.674 | 8.094 | 29.754 | 24.582 | 86.147 | 48.528 | 0 | 326.620 | 20.004 | 209.427 | 319.263 | 1010 |
9 | 14.951 | 12.124 | 10.746 | 14.313 | 86.628 | 65.992 | 38.504 | 262.311 | 102.671 | 124.897 | 409.013 | 1090 |
10 | 12.068 | 14.793 | 22.851 | 16.660 | 83.597 | 72.197 | 0 | 282.772 | 102.626 | 40.000 | 498.795 | 1080 |
11 | 10.949 | 12.881 | 29.978 | 22.735 | 81.118 | 68.188 | 0 | 319.873 | 102.653 | 209.805 | 318.360 | 1100 |
12 | 12.959 | 14.548 | 12.827 | 23.469 | 85.279 | 71.807 | 43.305 | 322.807 | 102.587 | 294.706 | 229.505 | 1150 |
13 | 7.645 | 6.000 | 23.631 | 17.610 | 66.860 | 37.085 | 0 | 290.082 | 102.277 | 294.397 | 319.2940 | 1110 |
14 | 12.479 | 12.934 | 10.477 | 23.523 | 86.153 | 68.327 | 38.361 | 323.010 | 154.915 | 40.0035 | 319.270 | 1030 |
15 | 5.250 | 10.724 | 10.642 | 23.184 | 51.663 | 61.030 | 38.454 | 321.706 | 102.663 | 294.730 | 139.783 | 1010 |
16 | 14.999 | 14.999 | 14.427 | 24.872 | 89.021 | 72.499 | 36.103 | 313.277 | 20.000 | 209.811 | 319.274 | 1060 |
17 | 14.489 | 11.211 | 16.659 | 24.999 | 86.612 | 62.890 | 30.688 | 327.847 | 102.638 | 209.830 | 229.509 | 1050 |
18 | 14.999 | 14.990 | 10.003 | 20.425 | 86.620 | 72.486 | 38.052 | 308.464 | 174.906 | 209.925 | 229.517 | 1120 |
19 | 11.788 | 9.4846 | 28.025 | 24.983 | 82.931 | 55.652 | 0 | 327.803 | 164.339 | 209.750 | 229.523 | 1070 |
20 | 14.671 | 6.787 | 12.142 | 24.791 | 86.640 | 41.686 | 42.707 | 327.2481 | 102.671 | 40.000 | 409.035 | 1050 |
21 | 6.073 | 14.969 | 29.999 | 24.984 | 55.318 | 72.457 | 0 | 327.806 | 20.000 | 294.674 | 139.751 | 910 |
22 | 14.999 | 13.959 | 12.685 | 18.017 | 86.620 | 70.717 | 38.253 | 293.043 | 102.663 | 40.007 | 228.700 | 860 |
23 | 8.985 | 9.7949 | 10.115 | 22.697 | 72.635 | 57.085 | 38.099 | 319.711 | 102.658 | 209.802 | 50.007 | 850 |
24 | 10.875 | 14.999 | 16.860 | 24.925 | 95.751 | 80.948 | 54.837 | 303.378 | 174.997 | 40.096 | 50.000 | 800 |
Algorithm | Minimum Cost ($) | Average Cost ($) | Maximum Cost ($) |
---|---|---|---|
LAPO | 38,800.75 | 38,915.23 | 39,520 |
MDNLPSO [11] | 40,179 | 40,637 | 41,182 |
CPSO [30] | 40,204.32 | 40,592.73 | 40,831.55 |
TLPSOS [36] | 40,298.28 | 40,298.28 | 40,298.28 |
ALO [26] | 40,780.05 | 41,094.3414 | 40,905.8259 |
ORCCRO [39] | 40,936.65 | 41,127.6819 | 40,944.2938 |
MCDE [6] | 40,945.75 | 41,380.54 | 41,977.04 |
ACABC [9] | 41,074.42 | NA | NA |
RCCRO [39] | 41,497.85 | 41,502.3669 | 41,498.2129 |
DGSA [40] | 41,751.15 | 41,989.02 | 41,821.49 |
CSA [41] | 42,244.057 | NA | NA |
MDE [42] | 42,611.14 | NA | NA |
PSO [43] | 44,740 | NA | NA |
DE [42] | 44,526.10 | NA | NA |
EP [34] | 45,063.004 | NA | NA |
Hours (h) | Hydro Power (MW) | Thermal Power (MW) | RE (MW) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Qh1 | Qh2 | Qh3 | Qh4 | Ph1 | Ph2 | Ph3 | Ph4 | Ps1 | Ps2 | Ps3 | PW | PPV | |
1 | 9.214 | 11.549 | 17.709 | 14.811 | 82.387 | 76.720 | 32.173 | 213.054 | 102.571 | 124.750 | 50.023 | 68.322 | 0.000 |
2 | 8.346 | 13.687 | 11.911 | 18.839 | 77.682 | 78.995 | 38.624 | 216.981 | 102.667 | 125.000 | 139.579 | 0.471 | 0.000 |
3 | 14.193 | 13.851 | 12.169 | 24.678 | 95.500 | 75.487 | 38.541 | 199.442 | 20.039 | 124.891 | 50.611 | 95.489 | 0.000 |
4 | 14.220 | 12.885 | 14.895 | 16.886 | 91.504 | 69.912 | 35.216 | 176.028 | 102.677 | 124.414 | 50.187 | 0.062 | 0.000 |
5 | 13.870 | 14.851 | 10.651 | 16.432 | 86.411 | 72.285 | 40.201 | 239.963 | 21.040 | 40.048 | 139.760 | 30.292 | 0.000 |
6 | 14.899 | 14.466 | 14.094 | 20.989 | 86.636 | 71.666 | 36.656 | 311.552 | 20.139 | 125.324 | 139.808 | 8.219 | 0.000 |
7 | 12.497 | 14.848 | 12.257 | 21.012 | 84.489 | 72.280 | 40.319 | 311.675 | 102.908 | 124.833 | 139.044 | 55.117 | 19.335 |
8 | 13.760 | 14.968 | 27.689 | 24.915 | 86.222 | 72.455 | 0.000 | 327.607 | 101.950 | 209.887 | 141.301 | 24.918 | 45.660 |
9 | 14.102 | 13.266 | 12.985 | 24.794 | 86.461 | 69.171 | 38.014 | 327.257 | 102.080 | 209.225 | 139.617 | 51.327 | 66.849 |
10 | 14.698 | 11.287 | 12.181 | 24.731 | 86.642 | 63.165 | 38.536 | 327.070 | 102.492 | 209.928 | 139.937 | 34.530 | 77.700 |
11 | 5.568 | 14.985 | 11.813 | 24.755 | 53.512 | 72.479 | 38.646 | 327.140 | 103.595 | 40.865 | 319.245 | 47.760 | 96.758 |
12 | 9.268 | 11.928 | 24.017 | 24.962 | 77.378 | 65.369 | 0.000 | 327.743 | 102.440 | 124.195 | 319.332 | 33.382 | 100.160 |
13 | 13.923 | 9.859 | 24.269 | 22.203 | 89.011 | 57.372 | 0.000 | 317.535 | 102.291 | 208.071 | 228.475 | 0.699 | 106.545 |
14 | 14.015 | 8.542 | 13.182 | 24.768 | 87.832 | 51.307 | 38.563 | 327.178 | 102.924 | 209.795 | 50.003 | 50.578 | 111.820 |
15 | 12.347 | 14.105 | 14.311 | 24.698 | 84.717 | 71.007 | 42.464 | 326.969 | 102.577 | 210.031 | 50.059 | 40.255 | 81.921 |
16 | 14.169 | 14.878 | 12.355 | 24.979 | 86.496 | 72.325 | 46.364 | 327.792 | 102.600 | 124.843 | 140.478 | 128.744 | 30.358 |
17 | 14.169 | 14.878 | 12.355 | 24.979 | 86.496 | 72.325 | 47.449 | 327.792 | 102.600 | 124.843 | 140.478 | 117.659 | 30.358 |
18 | 11.599 | 13.383 | 29.762 | 24.953 | 82.442 | 69.451 | 0.000 | 327.717 | 102.436 | 208.437 | 316.964 | 0.000 | 12.578 |
19 | 14.358 | 13.659 | 10.378 | 23.671 | 86.575 | 70.083 | 50.714 | 314.179 | 20.040 | 293.928 | 229.887 | 4.596 | 0.000 |
20 | 10.979 | 11.158 | 14.787 | 17.918 | 80.634 | 62.695 | 50.447 | 285.915 | 102.682 | 124.674 | 318.791 | 24.162 | 0.000 |
21 | 10.802 | 12.270 | 29.105 | 22.065 | 80.059 | 66.442 | 0.000 | 306.975 | 101.140 | 124.853 | 230.298 | 0.233 | 0.000 |
22 | 14.492 | 13.813 | 18.592 | 20.909 | 86.613 | 70.416 | 23.588 | 311.124 | 101.058 | 125.484 | 138.634 | 3.084 | 0.000 |
23 | 13.513 | 14.921 | 28.134 | 22.546 | 85.989 | 72.388 | 0.000 | 309.510 | 102.278 | 125.034 | 139.843 | 14.959 | 0.000 |
24 | 7.005 | 11.643 | 10.194 | 24.448 | 72.180 | 72.364 | 56.414 | 302.196 | 102.296 | 40.040 | 139.651 | 14.859 | 0.000 |
Total cost = $38,210.073 |
Hours (h) | Hydro Power (MW) | |||||||
---|---|---|---|---|---|---|---|---|
Qh1 | Qh2 | Qh3 | Qh4 | Ph1 | Ph2 | Ph3 | Ph4 | |
1 | 6.760 | 12.010 | 12.396 | 22.714 | 67.493 | 78.042 | 41.173 | 243.511 |
2 | 5.446 | 13.840 | 19.180 | 19.813 | 57.668 | 78.867 | 20.980 | 208.461 |
3 | 10.334 | 13.490 | 11.538 | 24.814 | 89.058 | 74.456 | 38.675 | 199.517 |
4 | 7.351 | 14.801 | 15.407 | 24.734 | 71.952 | 72.209 | 34.096 | 199.474 |
5 | 8.261 | 9.964 | 15.398 | 18.032 | 77.287 | 57.842 | 34.118 | 253.373 |
6 | 8.672 | 11.778 | 17.941 | 24.901 | 79.209 | 64.875 | 26.228 | 298.063 |
7 | 6.503 | 12.264 | 10.376 | 17.186 | 65.189 | 66.423 | 38.296 | 286.888 |
8 | 8.208 | 14.965 | 12.397 | 24.995 | 77.135 | 72.450 | 38.434 | 327.835 |
9 | 11.174 | 8.820 | 12.778 | 21.182 | 91.325 | 52.392 | 38.185 | 312.563 |
10 | 13.096 | 14.794 | 12.438 | 24.982 | 95.848 | 72.199 | 38.411 | 327.800 |
11 | 12.535 | 14.764 | 11.850 | 24.920 | 94.370 | 72.152 | 44.236 | 327.621 |
12 | 7.391 | 10.933 | 13.414 | 22.485 | 71.490 | 61.845 | 37.576 | 318.797 |
13 | 9.678 | 12.937 | 11.354 | 24.851 | 85.353 | 68.334 | 42.941 | 327.424 |
14 | 6.230 | 13.024 | 14.458 | 24.132 | 64.456 | 68.563 | 39.095 | 325.170 |
15 | 11.994 | 11.273 | 10.280 | 24.888 | 96.367 | 63.117 | 38.229 | 312.290 |
16 | 8.689 | 14.972 | 29.838 | 24.968 | 81.714 | 72.461 | 0.000 | 327.758 |
17 | 13.171 | 12.519 | 22.438 | 24.287 | 98.328 | 67.179 | 2.786 | 320.525 |
18 | 10.784 | 9.906 | 12.669 | 24.989 | 89.995 | 57.582 | 38.265 | 327.789 |
19 | 10.022 | 14.670 | 11.550 | 24.924 | 85.627 | 72.005 | 38.674 | 327.634 |
20 | 6.862 | 6.643 | 19.986 | 23.930 | 66.834 | 40.874 | 17.696 | 324.478 |
21 | 9.640 | 9.382 | 10.295 | 17.871 | 82.517 | 55.943 | 38.240 | 291.995 |
22 | 9.895 | 14.454 | 12.722 | 23.527 | 82.935 | 71.647 | 38.227 | 323.023 |
23 | 12.989 | 14.809 | 17.387 | 24.938 | 90.712 | 72.221 | 28.280 | 327.675 |
24 | 11.357 | 13.412 | 24.417 | 24.699 | 97.803 | 77.733 | 20.806 | 302.835 |
Hours (h) | Thermal Power (MW) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Ps1 | Ps2 | Ps3 | Ps4 | Ps5 | Ps6 | Ps7 | Ps8 | Ps9 | Ps10 | |
1 | 319.329 | 199.965 | 94.364 | 69.818 | 124.796 | 189.692 | 163.440 | 35.028 | 97.976 | 25.372 |
2 | 139.517 | 274.234 | 94.918 | 69.222 | 124.509 | 239.416 | 163.417 | 35.178 | 97.002 | 176.611 |
3 | 139.796 | 274.419 | 20.186 | 70.102 | 274.449 | 139.641 | 104.040 | 35.776 | 99.753 | 140.134 |
4 | 229.711 | 348.804 | 97.751 | 20.379 | 74.830 | 139.648 | 103.858 | 35.280 | 97.494 | 124.515 |
5 | 229.529 | 272.246 | 93.673 | 69.654 | 74.655 | 138.513 | 163.450 | 35.160 | 96.971 | 73.529 |
6 | 229.672 | 50.164 | 94.925 | 119.624 | 174.692 | 239.511 | 104.444 | 35.055 | 106.832 | 176.706 |
7 | 319.227 | 274.170 | 93.270 | 69.887 | 124.561 | 139.562 | 162.999 | 35.113 | 98.052 | 176.350 |
8 | 319.290 | 54.043 | 96.594 | 74.199 | 174.471 | 289.433 | 223.111 | 35.412 | 98.156 | 129.437 |
9 | 229.428 | 124.793 | 94.384 | 119.194 | 274.256 | 339.054 | 103.626 | 35.125 | 98.252 | 177.423 |
10 | 319.774 | 274.655 | 96.785 | 69.947 | 275.943 | 189.591 | 45.030 | 35.188 | 159.733 | 79.095 |
11 | 320.048 | 125.074 | 95.298 | 120.330 | 224.733 | 190.024 | 163.817 | 35.057 | 109.062 | 178.176 |
12 | 409.140 | 274.323 | 20.044 | 119.761 | 174.385 | 239.579 | 103.397 | 35.210 | 158.384 | 126.070 |
13 | 229.535 | 124.644 | 95.479 | 119.631 | 323.491 | 289.222 | 163.452 | 35.028 | 25.489 | 179.978 |
14 | 229.384 | 274.084 | 89.611 | 119.352 | 224.457 | 174.504 | 163.176 | 35.168 | 97.131 | 125.850 |
15 | 409.015 | 199.616 | 95.678 | 51.038 | 273.530 | 239.439 | 45.090 | 35.136 | 25.152 | 126.305 |
16 | 319.914 | 199.477 | 95.586 | 119.724 | 224.602 | 189.559 | 163.545 | 35.197 | 103.567 | 126.894 |
17 | 139.667 | 421.838 | 94.528 | 69.850 | 174.330 | 239.204 | 163.314 | 35.054 | 97.669 | 125.727 |
18 | 318.913 | 424.026 | 94.116 | 69.549 | 274.606 | 139.759 | 104.756 | 35.200 | 98.136 | 47.307 |
19 | 139.699 | 274.526 | 20.807 | 122.996 | 324.556 | 189.534 | 163.479 | 35.001 | 98.366 | 177.097 |
20 | 139.766 | 349.273 | 103.877 | 69.888 | 372.111 | 89.593 | 104.221 | 35.029 | 160.000 | 176.360 |
21 | 229.409 | 274.535 | 20.314 | 69.546 | 224.309 | 189.571 | 163.589 | 35.073 | 159.362 | 75.598 |
22 | 229.553 | 273.538 | 94.161 | 20.283 | 224.512 | 139.818 | 103.896 | 35.057 | 97.956 | 125.394 |
23 | 139.979 | 124.657 | 125.709 | 69.682 | 323.970 | 189.614 | 45.162 | 35.250 | 99.308 | 177.770 |
24 | 408.281 | 124.712 | 20.438 | 20.042 | 124.704 | 239.473 | 104.203 | 35.046 | 97.895 | 125.940 |
Algorithm | Minimum Cost ($) | Average Cost ($) | Maximum Cost ($) |
---|---|---|---|
LAPO | 161,746.4 | 160,445.4 | 161,935.4 |
ORCCRO [39] | 163,066.0337 | 163,068.7739 | 163,134.5391 |
RCCRO [39] | 164,138.6517 | 164,140.3997 | 164,182.3520 |
SPPSO [44] | 167,710.56 | 168,688.92 | 170,879.30 |
SPSO [44] | 189,350.63 | 190,560.31 | 191,844.28 |
MDE [44] | 177,338.60 | 179,676.35 | 182,172.01 |
DE [44] | 170,964.15 | NA | NA |
MCDE [6] | 165,331.7 | 166,116.4 | 167,060.6 |
IDE [29] | 170,576.5 | 170,589.6 | 170,608.3 |
Hours (h) | Hydro Power (MW) | |||||||
---|---|---|---|---|---|---|---|---|
Qh1 | Qh2 | Qh3 | Qh4 | Ph1 | Ph2 | Ph3 | Ph4 | |
1 | 7.925 | 11.136 | 15.490 | 17.354 | 75.249 | 75.421 | 47.159 | 227.490 |
2 | 5.078 | 8.343 | 14.311 | 21.083 | 54.305 | 61.768 | 36.305 | 219.114 |
3 | 10.601 | 14.585 | 12.904 | 23.173 | 89.848 | 80.999 | 38.084 | 197.853 |
4 | 5.035 | 14.937 | 10.163 | 23.248 | 53.819 | 76.729 | 38.139 | 197.966 |
5 | 9.371 | 12.213 | 14.935 | 20.424 | 83.602 | 66.927 | 35.134 | 227.198 |
6 | 7.893 | 14.849 | 17.662 | 18.952 | 74.767 | 72.282 | 27.285 | 288.448 |
7 | 7.700 | 12.670 | 19.807 | 24.977 | 73.598 | 67.610 | 17.971 | 327.784 |
8 | 7.617 | 14.965 | 12.444 | 24.949 | 73.424 | 72.450 | 38.407 | 327.706 |
9 | 9.724 | 9.908 | 11.767 | 24.971 | 85.735 | 57.592 | 38.654 | 327.768 |
10 | 7.420 | 11.803 | 15.315 | 15.756 | 73.029 | 64.957 | 34.309 | 275.292 |
11 | 11.805 | 12.253 | 13.303 | 21.505 | 95.566 | 66.390 | 37.699 | 314.207 |
12 | 12.573 | 14.425 | 10.641 | 24.884 | 96.840 | 71.595 | 38.454 | 327.518 |
13 | 5.281 | 13.149 | 10.977 | 23.574 | 56.699 | 68.882 | 38.593 | 323.198 |
14 | 10.655 | 13.712 | 11.106 | 24.824 | 92.592 | 70.199 | 38.628 | 327.344 |
15 | 7.839 | 14.589 | 12.495 | 24.839 | 77.490 | 71.875 | 38.378 | 327.389 |
16 | 12.480 | 12.249 | 14.955 | 24.290 | 99.433 | 66.379 | 35.094 | 325.690 |
17 | 10.413 | 11.508 | 10.692 | 24.870 | 91.299 | 63.953 | 38.479 | 327.478 |
18 | 9.809 | 11.459 | 12.541 | 24.985 | 87.891 | 63.780 | 38.350 | 327.809 |
19 | 11.788 | 14.915 | 12.980 | 24.958 | 94.466 | 72.379 | 38.018 | 327.731 |
20 | 12.334 | 14.378 | 11.587 | 23.847 | 93.418 | 71.513 | 38.825 | 324.188 |
21 | 6.813 | 14.810 | 15.299 | 22.369 | 66.486 | 72.223 | 34.345 | 318.285 |
22 | 10.775 | 12.098 | 13.103 | 17.363 | 87.322 | 65.910 | 44.132 | 288.231 |
23 | 12.974 | 14.599 | 12.428 | 24.829 | 91.633 | 71.891 | 47.674 | 327.360 |
24 | 13.248 | 13.390 | 22.845 | 24.330 | 103.979 | 77.677 | 30.710 | 301.884 |
Hours (h) | Thermal Power (MW) | RE (MW) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Ps1 | Ps2 | Ps3 | Ps4 | Ps5 | Ps6 | Ps7 | Ps8 | PW | PPV | |
1 | 318.954 | 124.729 | 20.295 | 119.772 | 224.470 | 189.373 | 163.447 | 35.046 | 128.594 | 0.000 |
2 | 319.204 | 199.490 | 94.699 | 119.729 | 274.595 | 189.569 | 104.305 | 35.018 | 71.901 | 0.000 |
3 | 409.050 | 199.469 | 94.804 | 119.806 | 124.718 | 89.731 | 163.589 | 35.039 | 57.009 | 0.000 |
4 | 318.863 | 274.326 | 94.814 | 69.773 | 174.555 | 89.699 | 163.398 | 35.030 | 62.889 | 0.000 |
5 | 139.716 | 274.361 | 94.885 | 119.779 | 124.720 | 289.084 | 163.466 | 35.030 | 16.097 | 0.000 |
6 | 229.527 | 349.173 | 94.792 | 20.002 | 224.382 | 139.288 | 104.094 | 35.211 | 140.749 | 0.000 |
7 | 229.463 | 274.415 | 94.673 | 119.744 | 274.411 | 239.455 | 104.165 | 35.050 | 74.084 | 17.578 |
8 | 319.457 | 124.946 | 94.690 | 119.736 | 324.078 | 139.814 | 222.600 | 35.001 | 68.185 | 49.506 |
9 | 408.844 | 199.612 | 94.827 | 69.784 | 174.546 | 239.541 | 163.433 | 35.007 | 139.598 | 55.060 |
10 | 227.804 | 349.206 | 94.654 | 69.714 | 224.281 | 239.431 | 163.565 | 35.096 | 141.773 | 86.892 |
11 | 319.096 | 348.906 | 91.073 | 119.106 | 224.369 | 89.717 | 163.312 | 35.053 | 117.605 | 77.900 |
12 | 139.747 | 348.787 | 20.258 | 69.993 | 174.635 | 239.439 | 281.758 | 35.280 | 201.329 | 104.366 |
13 | 319.311 | 199.617 | 94.858 | 70.001 | 324.266 | 239.510 | 163.518 | 35.198 | 73.874 | 102.474 |
14 | 319.276 | 273.995 | 94.863 | 119.828 | 74.873 | 239.589 | 104.270 | 65.497 | 100.768 | 108.276 |
15 | 229.371 | 199.615 | 94.800 | 69.740 | 224.442 | 239.345 | 163.326 | 81.612 | 92.618 | 100.000 |
16 | 139.556 | 348.993 | 94.357 | 69.838 | 374.046 | 189.469 | 211.563 | 35.222 | 0.359 | 70.000 |
17 | 229.473 | 199.584 | 20.049 | 119.624 | 323.928 | 238.441 | 162.997 | 35.007 | 149.688 | 50.000 |
18 | 319.281 | 349.163 | 20.012 | 69.952 | 323.873 | 189.469 | 163.467 | 35.010 | 111.943 | 20.000 |
19 | 229.989 | 275.560 | 94.824 | 119.889 | 224.421 | 139.663 | 222.982 | 35.115 | 194.962 | 0.000 |
20 | 139.536 | 349.005 | 94.735 | 119.753 | 373.954 | 188.513 | 104.283 | 35.036 | 117.229 | 0.000 |
21 | 139.913 | 349.328 | 94.877 | 69.823 | 174.495 | 239.085 | 281.896 | 35.002 | 34.240 | 0.000 |
22 | 229.447 | 274.283 | 94.236 | 69.878 | 224.328 | 338.203 | 104.277 | 35.295 | 4.457 | 0.000 |
23 | 140.274 | 199.654 | 94.907 | 70.537 | 274.360 | 289.342 | 104.221 | 35.010 | 103.137 | 0.000 |
24 | 229.062 | 124.378 | 94.552 | 119.675 | 224.191 | 89.683 | 222.729 | 35.001 | 146.479 | 0.000 |
Total cost = $158,572.8 |
Hours (h) | Hydro Power (MW) | |||||||
---|---|---|---|---|---|---|---|---|
Qh1 | Qh2 | Qh3 | Qh4 | Ph1 | Ph2 | Ph3 | Ph4 | |
1 | 13.316 | 7.132 | 11.064 | 22.027 | 95.066 | 57.177 | 41.893 | 242.550 |
2 | 7.040 | 12.185 | 28.964 | 24.946 | 68.327 | 79.129 | 0.000 | 213.308 |
3 | 12.744 | 11.740 | 13.309 | 18.662 | 92.605 | 75.627 | 37.694 | 184.675 |
4 | 7.893 | 14.223 | 11.299 | 21.508 | 72.162 | 78.542 | 38.663 | 194.459 |
5 | 9.245 | 12.197 | 13.519 | 24.784 | 78.394 | 69.949 | 38.921 | 268.703 |
6 | 5.009 | 13.766 | 12.985 | 24.913 | 50.562 | 70.315 | 42.524 | 327.603 |
7 | 8.443 | 14.087 | 11.702 | 24.675 | 74.779 | 70.971 | 38.663 | 316.807 |
8 | 6.605 | 11.315 | 10.069 | 24.565 | 63.751 | 63.267 | 38.061 | 326.566 |
9 | 11.825 | 14.696 | 10.162 | 24.809 | 89.352 | 72.046 | 38.138 | 326.801 |
10 | 7.516 | 9.069 | 12.159 | 24.439 | 70.567 | 53.646 | 38.545 | 315.488 |
11 | 12.529 | 8.077 | 27.485 | 24.431 | 92.583 | 49.146 | 0.000 | 326.146 |
12 | 11.663 | 14.945 | 11.957 | 24.967 | 89.493 | 72.422 | 38.612 | 327.758 |
13 | 5.014 | 12.388 | 19.548 | 22.084 | 52.444 | 66.798 | 19.242 | 316.991 |
14 | 14.496 | 12.684 | 10.880 | 24.986 | 96.493 | 67.650 | 38.560 | 327.810 |
15 | 7.929 | 8.042 | 10.029 | 24.885 | 74.595 | 48.980 | 38.026 | 327.522 |
16 | 13.486 | 14.917 | 11.407 | 24.948 | 95.129 | 72.381 | 38.672 | 327.704 |
17 | 13.720 | 8.489 | 15.930 | 23.143 | 93.003 | 50.665 | 32.787 | 321.546 |
18 | 9.791 | 8.562 | 11.804 | 24.508 | 80.948 | 51.054 | 38.647 | 326.388 |
19 | 5.540 | 14.547 | 11.370 | 24.852 | 54.812 | 71.805 | 38.670 | 327.425 |
20 | 9.321 | 11.304 | 27.960 | 24.982 | 77.946 | 63.228 | 0.000 | 327.798 |
21 | 14.980 | 13.563 | 14.761 | 18.274 | 86.624 | 69.868 | 35.484 | 294.858 |
22 | 8.133 | 14.743 | 15.343 | 24.659 | 68.189 | 72.121 | 34.245 | 326.854 |
23 | 13.571 | 14.905 | 12.201 | 24.985 | 86.048 | 72.364 | 38.527 | 327.807 |
24 | 10.661 | 8.840 | 13.440 | 23.732 | 94.775 | 60.017 | 58.977 | 300.161 |
Hours (h) | Thermal Power (MW) | RE (MW) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Ps1 | Ps2 | Ps3 | Ps4 | Ps5 | Ps6 | Ps7 | Ps8 | Pw1 | Pw2 | |
1 | 229.470 | 200.541 | 94.834 | 69.932 | 124.742 | 89.819 | 163.333 | 40.792 | 149.957 | 149.893 |
2 | 229.372 | 424.056 | 94.811 | 69.837 | 224.497 | 89.886 | 104.258 | 35.106 | 114.686 | 32.727 |
3 | 229.408 | 274.023 | 94.608 | 69.772 | 125.020 | 140.117 | 104.394 | 35.091 | 117.125 | 119.842 |
4 | 229.556 | 199.458 | 94.795 | 70.084 | 124.289 | 139.960 | 163.541 | 35.001 | 120.003 | 89.516 |
5 | 229.573 | 124.768 | 94.967 | 20.454 | 174.602 | 89.435 | 163.262 | 35.319 | 138.316 | 143.336 |
6 | 50.013 | 423.522 | 94.707 | 119.846 | 25.694 | 139.591 | 163.490 | 35.107 | 148.381 | 108.650 |
7 | 139.689 | 348.771 | 94.750 | 20.077 | 373.974 | 139.828 | 163.447 | 35.406 | 16.111 | 116.728 |
8 | 319.273 | 124.802 | 20.187 | 69.665 | 373.877 | 139.759 | 222.815 | 35.842 | 78.357 | 133.777 |
9 | 139.862 | 124.489 | 129.846 | 119.580 | 224.469 | 338.231 | 163.540 | 35.338 | 149.816 | 138.490 |
10 | 229.500 | 348.828 | 94.542 | 20.257 | 324.220 | 189.585 | 163.835 | 35.098 | 100.698 | 95.192 |
11 | 319.215 | 274.427 | 94.590 | 119.622 | 124.736 | 239.498 | 163.479 | 35.000 | 129.460 | 132.100 |
12 | 408.940 | 125.014 | 94.794 | 20.024 | 324.234 | 89.837 | 282.152 | 35.000 | 148.813 | 92.900 |
13 | 409.009 | 349.392 | 20.119 | 119.363 | 273.819 | 139.680 | 104.233 | 35.161 | 60.566 | 143.185 |
14 | 229.555 | 349.032 | 95.603 | 20.047 | 224.895 | 139.826 | 163.484 | 35.249 | 99.160 | 142.637 |
15 | 408.708 | 199.218 | 94.793 | 69.507 | 223.647 | 90.048 | 222.821 | 35.035 | 34.289 | 142.813 |
16 | 409.009 | 274.461 | 94.783 | 120.265 | 224.447 | 289.530 | 46.073 | 35.050 | 16.403 | 16.093 |
17 | 319.324 | 423.606 | 94.803 | 69.505 | 324.296 | 139.724 | 45.118 | 35.004 | 27.117 | 73.502 |
18 | 409.174 | 349.304 | 94.776 | 69.594 | 469.443 | 89.984 | 45.043 | 35.066 | 15.594 | 44.985 |
19 | 50.019 | 199.425 | 94.995 | 70.084 | 274.228 | 289.226 | 282.004 | 35.074 | 138.649 | 143.550 |
20 | 409.072 | 274.738 | 94.801 | 69.838 | 174.355 | 189.540 | 222.792 | 35.243 | 52.524 | 58.134 |
21 | 319.252 | 198.770 | 95.208 | 69.919 | 224.434 | 239.368 | 45.052 | 35.022 | 145.296 | 50.771 |
22 | 408.780 | 199.649 | 94.587 | 69.719 | 223.288 | 139.596 | 163.533 | 35.074 | 23.587 | 0.814 |
23 | 229.948 | 274.441 | 31.281 | 119.662 | 224.488 | 90.843 | 104.347 | 40.366 | 147.501 | 62.377 |
24 | 319.176 | 334.651 | 20.783 | 20.084 | 74.685 | 89.384 | 104.262 | 35.038 | 146.505 | 141.502 |
Total cost = $158,342.4 |
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Mohamed, M.; Youssef, A.-R.; Kamel, S.; Ebeed, M.; Elattar, E.E. Optimal Scheduling of Hydro–Thermal–Wind–Photovoltaic Generation Using Lightning Attachment Procedure Optimizer. Sustainability 2021, 13, 8846. https://doi.org/10.3390/su13168846
Mohamed M, Youssef A-R, Kamel S, Ebeed M, Elattar EE. Optimal Scheduling of Hydro–Thermal–Wind–Photovoltaic Generation Using Lightning Attachment Procedure Optimizer. Sustainability. 2021; 13(16):8846. https://doi.org/10.3390/su13168846
Chicago/Turabian StyleMohamed, Maha, Abdel-Raheem Youssef, Salah Kamel, Mohamed Ebeed, and Ehab E. Elattar. 2021. "Optimal Scheduling of Hydro–Thermal–Wind–Photovoltaic Generation Using Lightning Attachment Procedure Optimizer" Sustainability 13, no. 16: 8846. https://doi.org/10.3390/su13168846