Grey Wolf Optimizer for RES Capacity Factor Maximization at the Placement Planning Stage
Abstract
:1. Introduction
- 0.14—for solar generation power plants;
- 0.27—for wind generation power plants.
- forecasting the generation and installed capacity utilization factor of power plants with RES;
- choosing the optimal location for power plants with RES in order to maximize the installed capacity utilization factor.
2. Materials and Methods
2.1. Capacity Factor Forecasting
- Pinst is the installed capacity of the RES generation power facility, MW;
- SWDIFF is the diffuse (light energy scattered out of the direction of the sun) solar irradiance incident on a horizontal plane at the surface of the Earth under all sky conditions, kW/m2;
- SWDNI is the direct solar radiation incident on a horizontal plane on the Earth’s surface, kW/m2;
- SWDWN is the total solar radiation incident on a horizontal plane on the Earth’s surface, kW/m2;
- RH2M is the ratio of the actual partial pressure of water vapor to the partial pressure at saturation at a height of 2 m (relative humidity), %;
- T2M is the average air temperature at a height of 2 m above the ground, °C;
- SRFALB is the ratio of solar energy reflected by the Earth’s surface to the total solar energy incident on the Earth’s surface, p.u.;
- WS10M, WS50M is the average annual wind speed at a height of 10 and 50 m above the ground, respectively, m/s;
- Latitude is the value of geographic latitude characterizing the location of the power facility, deg;
- Longitude is the value of geographic longitude characterizing the location of the power facility, deg;
- CF is the installed capacity utilization factor of the power facility, p.u.
2.2. RES Placement Optimization
- at the first step of the hierarchy is the alpha wolf;
- the beta wolf is located on the second step of the hierarchy;
- the third most important in the pack is the delta wolf;
- the remaining individuals are equal and are called omega wolves.
3. Results
3.1. Capacity Factor Forecasting
3.2. RES Placement Optimization
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
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Wind Power Plants | |||||||||
---|---|---|---|---|---|---|---|---|---|
Pinst | Latitude | Longitude | RH2M | T2M | WS10M | WS50M | CF | ||
3.49 | xxxx | xxxx | 88.147 | 5.822 | 2.452 | 4.618 | 0.357 | ||
3.30 | xxxx | xxxx | 83.383 | 7.603 | 4.540 | 6.538 | 0.353 | ||
2.50 | xxxx | xxxx | 88.147 | 5.822 | 2.452 | 4.618 | 0.356 | ||
1.75 | xxxx | xxxx | 83.383 | 7.603 | 4.540 | 6.538 | 0.353 | ||
35 | xxxx | xxxx | 82.207 | 4.593 | 4.970 | 6.705 | 0.281 | ||
1.65 | xxxx | xxxx | 84.822 | 2.848 | 4.740 | 6.703 | 0.068 | ||
25.20 | xxxx | xxxx | 82.207 | 4.593 | 4.970 | 6.705 | 0.290 | ||
25.20 | xxxx | xxxx | 82.207 | 4.593 | 4.970 | 6.705 | 0.316 | ||
49.40 | xxxx | xxxx | 70.970 | 9.735 | 4.532 | 6.440 | 0.318 | ||
Solar Power Plants | |||||||||
Pinst | Latitude | Longitude | SWDIFF | SWDNI | SWDWN | SRFALB | RH2M | T2M | CF |
0.50 | xxxx | xxxx | 1.498 | 3.157 | 3.107 | 0.198 | 82.948 | 7.027 | 0.164 |
0.87 | xxxx | xxxx | 1.498 | 3.157 | 3.107 | 0.198 | 82.948 | 7.027 | 0.165 |
0.63 | xxxx | xxxx | 1.498 | 3.157 | 3.107 | 0.198 | 82.948 | 7.027 | 0.164 |
2 | xxxx | xxxx | 1.498 | 3.157 | 3.107 | 0.198 | 85.228 | 6.347 | 0.164 |
25 | xxxx | xxxx | 1.500 | 3.668 | 3.325 | 0.218 | 79.032 | 5.080 | 0.149 |
15 | xxxx | xxxx | 1.573 | 4.115 | 3.707 | 0.263 | 69.752 | 7.543 | 0.151 |
10 | xxxx | xxxx | 1.573 | 4.115 | 3.707 | 0.263 | 71.468 | 7.000 | 0.153 |
45 | xxxx | xxxx | 1.592 | 3.743 | 3.465 | 0.273 | 75.365 | 4.917 | 0.132 |
Wind Power Plants | ||
---|---|---|
Model | Number of Estimators | Maximum Features |
Random forest | 61 | 3 |
Solar Power Plants | ||
Model | Number of Estimators | Maximum Features |
Random forest | 141 | 4 |
Cross-Validation Results | |||
---|---|---|---|
RMSE, p.u. | Max_Error, p.u. | nMAE, % | Explained Variance, % |
0.1302 | 0.2082 | 52.8 | 86.6 |
0.0519 | 0.1242 | 24.9 | 97.9 |
0.0633 | 0.1555 | 32.5 | 95.4 |
0.0229 | 0.0502 | 5.2 | 81.4 |
0.0523 | 0.1348 | 11.7 | 96.9 |
Test Data Results | |||
RMSE, p.u. | Max_Error, p.u. | nMAE, % | Explained Variance, % |
0.0189 | 0.06 | 2.8 | 85.3 |
Cross-Validation Results | |||
---|---|---|---|
RMSE, p.u. | Max_Error, p.u. | nMAE, % | Explained Variance, % |
0.0071 | 0.015 | 3.6 | 72.5 |
0.0091 | 0.0202 | 3.9 | 57.4 |
0.0098 | 0.0191 | 5.1 | 42.8 |
0.0206 | 0.0611 | 11.3 | 30.7 |
0.0071 | 0.0167 | 2.9 | 75.2 |
Test Data Results | |||
RMSE, p.u. | Max_Error, p.u. | nMAE, % | Explained Variance, % |
0.006 | 0.0204 | 2.5 | 76.4 |
Run | Greedy GWO | Basic GWO | ||||||
---|---|---|---|---|---|---|---|---|
Initial Best | Final Best | Difference | Inside | Initial Best | Final Best | Difference | Inside | |
1 | 0.3497 | 0.4091 | 0.0594 | Yes | 0.5977 | 0.3374 | −0.2603 | Yes |
2 | 0.5179 | 0.7219 | 0.2040 | Yes | 0.3463 | 0.3443 | −0.0020 | No |
3 | 0.3491 | 0.4091 | 0.0600 | Yes | 0.3723 | 0.3186 | −0.0537 | No |
4 | 0.3533 | 0.3971 | 0.0437 | Yes | 0.3448 | 0.3205 | −0.0243 | No |
5 | 0.3488 | 0.7449 | 0.3961 | Yes | 0.3502 | 0.3492 | −0.0010 | Yes |
6 | 0.5978 | 0.7449 | 0.1471 | Yes | 0.3971 | 0.3450 | −0.0521 | Yes |
7 | 0.5180 | 0.7449 | 0.2269 | Yes | 0.5179 | 0.3389 | −0.1790 | Yes |
8 | 0.6756 | 0.6756 | 0 | Yes | 0.3502 | 0.6572 | 0.3070 | Yes |
9 | 0.6067 | 0.7219 | 0.1151 | Yes | 0.5979 | 0.3504 | −0.2475 | Yes |
10 | 0.3412 | 0.7449 | 0.4037 | Yes | 0.3750 | 0.3176 | −0.0574 | No |
Average maximization | 0.1656 | Average maximization | −0.0570 |
Algorithm | ||||
---|---|---|---|---|
Metric | Random Search | PSO | FFO | GWO |
Mean | 0.207699 | 0.466938 | 0.459489 | 0.480645 |
Median | 0.205152 | 0.493582 | 0.409117 | 0.397110 |
Standard deviation | 0.009906 | 0.009906 | 0.137109 | 0.146610 |
Maximal | 0.146610 | 0.527894 | 0.527894 | 0.744965 |
Minimal | 0.195894 | 0.195894 | 0.195894 | 0.324952 |
Mean deviation from global maximum | −0.532301 | −0.273062 | −0.280511 | −0.259355 |
Median deviation from global maximum | −0.534848 | −0.246418 | −0.330883 | −0.342890 |
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Bramm, A.M.; Eroshenko, S.A.; Khalyasmaa, A.I.; Matrenin, P.V. Grey Wolf Optimizer for RES Capacity Factor Maximization at the Placement Planning Stage. Mathematics 2023, 11, 2545. https://doi.org/10.3390/math11112545
Bramm AM, Eroshenko SA, Khalyasmaa AI, Matrenin PV. Grey Wolf Optimizer for RES Capacity Factor Maximization at the Placement Planning Stage. Mathematics. 2023; 11(11):2545. https://doi.org/10.3390/math11112545
Chicago/Turabian StyleBramm, Andrey M., Stanislav A. Eroshenko, Alexandra I. Khalyasmaa, and Pavel V. Matrenin. 2023. "Grey Wolf Optimizer for RES Capacity Factor Maximization at the Placement Planning Stage" Mathematics 11, no. 11: 2545. https://doi.org/10.3390/math11112545