Micro-Siting of Wind Turbines in an Optimal Wind Farm Area Using Teaching–Learning-Based Optimization Technique
Abstract
:1. Introduction
- Minimization of the land area of wind farm
- Maximization of the power production
- Minimization of the total cost
2. Materials and Methods
2.1. Jensen’s Wake Effect Modeling
2.2. Fitness Evaluation
2.2.1. Wind Farm Cost Estimation
2.2.2. Wind Farm Power Estimation
2.2.3. Evaluation of Fitness Function
2.2.4. Calculation of Efficiency
- .
2.3. Elitist Teaching–Learning-Based Optimization Algorithm
2.4. Different Wind Scenarios
2.4.1. Scenario-I: Uni-Directional Wind with the Identical Velocity
2.4.2. Scenario-II: Multi-Directional Wind with the Identical Velocity
2.4.3. Scenario-III: Multi-Directional Wind with Variable Wind Velocity
3. Results
3.1. Case 1 vs. WFAO–ETLBO
3.2. Case 2 vs. WFAO–ETLBO
3.3. Case 3 vs. WFAO–ETLBO
4. Conclusions
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
WFAO | Wind farm area optimization |
ETLBO | Elitist Teaching–Learning-Based Optimization |
undisturbed/freestream wind speed | |
a | interference coefficient/induction/perturbation coefficient |
rotor radius | |
downstream rotor radius | |
d | rotor diameter |
x | wind downstream distance |
wake spread angle | |
entrainment constant | |
K.E. | kinetic energy |
N | number of turbines |
P | actual power of wind turbine |
ideal power of wind turbine | |
density | |
velocity of the turbine with multiple wake effect | |
efficiency of wind farm | |
power with multiple wake effects | |
power without wake effects | |
Lmean | Mean of a learner |
Lteacher | Best learner identified as a teacher |
Teaching factor | |
Uniformly distributed random | |
ith learner | |
jth learner | |
Fitness value of learner | |
ε | convergence criteria |
R.C. | relative change |
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Scenario-I | Scenario-II | Scenario-III | ||||
---|---|---|---|---|---|---|
Mosetti et al. | WFAO–ETLBO | Mosetti et al. | WFAO–ETLBO | Mosetti et al. | WFAO–ETLBO | |
Number of turbines | 26 | 26 | 19 | 19 | 15 | 15 |
Number of individuals | 200 | 100 | 200 | 100 | 200 | 100 |
Fitness value | 0.001619 | 0.0015868 | 0.0017371 | 0.0019232 | 0.00099405 | 0.0010977 |
Total Power (KW/year) (R.C. (%)) | 12,352 | 12,607.9 (2.07) | 9244 | 8343.51 (9.74) | 13,460 | 12,116.91 (9.97) |
Efficiency (%) (R.C. (%)) | 91.65 | 93.54 (2.07) | 93.851 | 84.71 (9.74) | 94.62 | 85.85 (9.26) |
Converged number of iterations | 400 | 75 | 350 | 15 | 400 | 15 |
Area Used (m) | 2000 × 2000 | 1385 × 1385 | 2000 × 2000 | 1095 × 1095 | 2000 × 2000 | 966 × 966 |
% Reduction in Area | ~ | 30.75 | ~ | 45.25 | ~ | 51.75 |
Simulation Time (s) | Not reported | 480.2 | Not reported | 708.7 | Not reported | 534.5 |
Scenario-I | Scenario-II | Scenario-III | ||||
---|---|---|---|---|---|---|
Grady et al. | WFAO–ETLBO | Grady et al. | WFAO–ETLBO | Grady et al. | WFAO–ETLBO | |
Number of turbines | 30 | 30 | 39 | 39 | 39 | 39 |
Number of individuals | 600 | 100 | 600 | 100 | 600 | 100 |
Fitness value | 0.0015436 | 0.0015812 | 0.0015666 | 0.0015800 | 0.0008403 | 0.0008665 |
Total Power (KW/year) (R.C. (%)) | 14,310 | 13,969.59 (2.37) | 17,220 | 17,039.24 (1.05) | 32,038 | 31,068.72 (3.02) |
Efficiency (%) (R.C. (%)) | 92.015 | 89.83 (2.37) | 85.174 | 84.28 (1.05) | 86.619 | 84.32 (2.65) |
Converged number of iterations | 1203 | 15 | 3000 | 20 | 1000 | 30 |
Area Used (m) | 2000 × 2000 | 1385 × 1385 | 2000 × 2000 | 1856 × 1856 | 2000 × 2000 | 1856 × 1856 |
% Reduction in Area | ~ | 30.75 | ~ | 7.2 | ~ | 7.2 |
Simulation Time (s) | Not reported | 134.86 | Not reported | 4978.29 | Not reported | 4101.44 |
Scenario-I | Scenario-II | Scenario-III | ||||
---|---|---|---|---|---|---|
Mittal et al. | WFAO–ETLBO | Mittal et al. | WFAO–ETLBO | Mittal et al. | WFAO–ETLBO | |
Number of turbines | 44 | 44 | 38 | 38 | 41 | 41 |
Number of individuals | Not reported | 100 | Not reported | 100 | Not reported | 100 |
Fitness value | 0.0013602 | 0.0015101 | 0.0015273 | 0.0015699 | 0.00084379 | 0.0008641 |
Total Power (KW/year) (R.C. (%)) | 21.936 | 20,758.66 (5.36) | 17,259 | 16,790.89 (2.71) | 33,262 | 32,482.32 (2.34) |
Efficiency (%) (R.C. (%)) | 96.17 | 90.62 (5.77) | 87.612 | 85.24 (2.71) | 86.729 | 83.85 (3.32) |
Converged number of iterations | Not reported | 23 | Not reported | 15 | Not reported | 20 |
Area Used (m) | 2000 × 2000 | 1856 × 1856 | 2000 × 2000 | 1856 × 1856 | 2000 × 2000 | 1856 × 1856 |
% Reduction in Area | ~ | 7.2 | ~ | 7.2 | ~ | 7.2 |
Simulation Time (s) | Not reported | 94.51 | Not reported | 1950.44 | Not reported | 3002.15 |
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Hussain, M.N.; Shaukat, N.; Ahmad, A.; Abid, M.; Hashmi, A.; Rajabi, Z.; Tariq, M.A.U.R. Micro-Siting of Wind Turbines in an Optimal Wind Farm Area Using Teaching–Learning-Based Optimization Technique. Sustainability 2022, 14, 8846. https://doi.org/10.3390/su14148846
Hussain MN, Shaukat N, Ahmad A, Abid M, Hashmi A, Rajabi Z, Tariq MAUR. Micro-Siting of Wind Turbines in an Optimal Wind Farm Area Using Teaching–Learning-Based Optimization Technique. Sustainability. 2022; 14(14):8846. https://doi.org/10.3390/su14148846
Chicago/Turabian StyleHussain, Muhammad Nabeel, Nadeem Shaukat, Ammar Ahmad, Muhammad Abid, Abrar Hashmi, Zohreh Rajabi, and Muhammad Atiq Ur Rehman Tariq. 2022. "Micro-Siting of Wind Turbines in an Optimal Wind Farm Area Using Teaching–Learning-Based Optimization Technique" Sustainability 14, no. 14: 8846. https://doi.org/10.3390/su14148846
APA StyleHussain, M. N., Shaukat, N., Ahmad, A., Abid, M., Hashmi, A., Rajabi, Z., & Tariq, M. A. U. R. (2022). Micro-Siting of Wind Turbines in an Optimal Wind Farm Area Using Teaching–Learning-Based Optimization Technique. Sustainability, 14(14), 8846. https://doi.org/10.3390/su14148846