Investigation of the layout of kilowatt-scale wind turbines located among megawatt-scale ones by means of an analytical model

Document Type : Mechanics article

Authors

1 Department of Mechanical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Mechanical Engineering, Central Tehran Branch, Islamic Azad University,Tehran, Iran

3 Department of Mechanical Engineering, Karaj Branch, Islamic Azad University, Karaj, Alborz, Iran

Abstract

The methods used for maximum exploitation of wind farms’ potentials can be classified into two categories: turbines layout optimization and utilization of turbines with different hub heights. The layout optimizations are generally performed by optimization algorithms. A drawback of these algorithms is their inability to render a single result as the optimized result. In the present study, by using an analytical model for 3D wind velocity distribution in the wake and including wake interactions, a model has been presented for estimation of the generated power of turbines implemented in wind farms. By coupling this model with the cost model of turbines' implementation, a function for the optimized layout has been presented. By calculating this function for different layouts of turbines in farms, the optimized layout can be obtained. In the present study, the calculations of turbines' layout optimization were carried out using a MATLAB-implemented code. By dividing the solution domain into grids and taking into account the minimum optimized distance of turbines from one another from the economical and power output aspects, the value of the layout optimization function has been calculated for different possible layouts. Finally, the layout of kilowatt-scaled turbines located among megawatt-scale ones for Horns Rev offshore farm has been modeled to obtain the maximum power output. From the results obtained for the optimized and maximum number of kilowatt-scaled turbines, it is inferred that the power of the farm has been increased by 7% (3.226 MW) by 35.7% efficiency and 9.35% (4.712 MW) by 34.06% efficiency,respectively.

Keywords

References

[1] سامان احمدی، ایمان پورفر و امین ساکی، "مدل سازی مزرعه بادی مجهز به ژنراتور القایی دوسوتغذیه با معادل سازی بخش مکانیکی با استفاده از خوشه بندی بر اساس ضریب جذب توان" نشریه مدل سازی در مهندسی، دوره 18، شماره 60، سال 1399، صفحه 169-182.
[2] آرش حاتمی و بهنام معتکف ایمانی، "کنترل توربین بادی محور افقی دارای ژنراتور سنکرون به منظور جذب بیشینه انرژی باد" نشریه مدل سازی در مهندسی، دوره 16، شماره 54، سال 1397، صفحه 403-413.
[3] جاماسب پیرکندی و رضا حربی منفرد، "شبیه سازی ترمودینامیکی یک سیستم هیبریدی توربین باد و پیل سوختی با کاربرد در یک سیستم مستقل از شبکه" نشریه مدل سازی در مهندسی، دوره 16، شماره 53، سال 1397، صفحه 25-37.
[4] M. Ge, Y. Wu, Y. Liu, and X. I. Yang, "A two-dimensional Jensen model with a Gaussian-shaped velocity deficit", Renewable Energy, vol. 141, 2019, pp. 46-56.
[5] R. J. Barthelmie and S. T. Frandsen, "Flow and wakes in large wind farms in complex terrain and    offshore,  Applied Energy, vol. 226, 2018, pp. 110-127..
[6] P. Sorensen and T. Nielsen, "Recalibrating wind turbine wake model parameters—validating the wake model performance for large offshore wind farms", European Wind Energy Conference and Exhibition, EWEA, 2006.
[7] C. L. Archer et al., "Review and evaluation of wake loss models for wind energy applications", Applied Energy, vol. 226, 2018, pp. 1187-1207.
[8] J. F. Manwell, J. G. McGowan, and A. L. Rogers, Wind energy explained: theory, design and application. John Wiley & Sons, 2010.
[9] I. Katic, J. Højstrup, and N. O. Jensen, "A simple model for cluster efficiency", European wind energy association conference and exhibition, 1987.
[10] J. K. Kaldellis, P. Triantafyllou, and P. Stinis, "Critical evaluation of Wind Turbines’ analytical wake models", Renewable and Sustainable Energy Reviews, vol. 144, 2021, p. 110991.
[11] R. Krishnamurthy, J. Reuder, B. Svardal, H. J. S. Fernando, and J. B. Jakobsen, "Offshore wind turbine wake characteristics using scanning doppler lidar", Energy Procedia, vol. 137, 2017, pp. 428-442.
[12] G. Marmidis, S. Lazarou, and E. Pyrgioti, "Optimal placement of wind turbines in a wind park using Monte Carlo simulation", Renewable energy, vol. 33, no. 7, 2008, pp. 1455-1460.
[13] A. Emami and P. Noghreh, "New approach on optimization in placement of wind turbines within wind farm by genetic algorithms", Renewable Energy, vol. 35, no. 7, 2010, pp. 1559-1564.
[14] R. Saidur, N. Rahim, M. Islam, and K. Solangi, "Environmental impact of wind energy", Renewable and sustainable energy reviews, vol. 15, no. 5, 2011, pp. 2423-2430.
[15] K. Siler-Evans, I. L. Azevedo, M. G. Morgan, and J. Apt, "Regional variations in the health, environmental, and climate benefits of wind and solar generation", Proceedings of the National Academy of Sciences, vol. 110, no. 29, 2013, pp. 11768-11773.
[16] P. M. Gebraad et al., "Wind plant power optimization through yaw control using a parametric model for wake effects—a CFD simulation study", Wind Energy, vol. 19, no. 1, 2016, pp. 95-114.
[17] J. Goit and J. Meyers, "Optimal control of energy extraction in wind-farm boundary layers", Journal of Fluid Mechanics, vol. 768, 2015, pp. 5-50.
[18] J. M. S. Bartl et al., "Wind tunnel experiments on wind turbine wakes in yaw: effects of inflow turbulence and shear", Wind Energy Science Discussions, vol. Volume: 3, Issue: 1, 2018, pp 329-343.
[19] L. Tian, W. Zhu, W. Shen, Y. Song, and N. Zhao, "Prediction of multi-wake problems using an improved Jensen wake model", Renewable energy, vol. 102, 2017, pp. 457-469.
[20] S. Naderi and F. Torabi, "Numerical investigation of wake behind a HAWT using modified actuator disc method", Energy Conversion and Management, vol. 1, 2017, pp. 1346-1357.
[21] L. Tian, W. Zhu, W. Shen, N. Zhao, and Z. Shen, "Development and validation of a new two-dimensional wake model for wind turbine wakes", Journal of Wind Engineering and Industrial Aerodynamics, vol. 137, 2015, pp. 90-99.
[22] M. Bastankhah and F. Porté-Agel, "A new analytical model for wind-turbine wakes", Renewable Energy, vol. 70, 2014, pp. 116-123.
[23] T. Ishihara, A. Yamaguchi, and Y. Fujino, "Development of a new wake model based on a wind tunnel experiment", Global wind power, vol. 105, no. 1, 2004, pp. 33-45.
[24] Y. Chen, H. Li, K. Jin, and Q. Song, "Wind farm layout optimization using genetic algorithm with different hub height wind turbines", Energy Conversion and Management, vol. 70, 2013, pp. 56-65.
[25] N. O. Jensen, "A note on wind generator interaction", Roskilde, Denmark: Risø National Laboratory for Sustainable Energy, 1983.
[26] S. Grady, M. Hussaini, and M. M. Abdullah, "Placement of wind turbines using genetic algorithms", Renewable energy, vol. 30, no. 2,  2005, pp. 259-270.
[27] S. Pookpunt and W. Ongsakul, "Optimal placement of wind turbines within wind farm using binary particle swarm optimization with time-varying acceleration coefficients", Renewable energy, vol. 55, 2013, pp. 266-276.
[28] L. Parada, C. Herrera, P. Flores, and V. Parada, "Wind farm layout optimization using a Gaussian-based wake model", Renewable energy, vol. 107, 2017, pp. 531-541.
[29] K. Chen, M. Song, X. Zhang, and S. Wang, "Wind turbine layout optimization with multiple hub height wind turbines using greedy algorithm", Renewable Energy, vol. 96, 2016, pp. 676-686.
[30] A. Mittal, "Optimization of the layout of large wind farms using a genetic algorithm", Master's thesis, Case Western Reserve University, 2010.
[31] K. Deb, "Evolutionary algorithms for multi-criterion optimization in engineering design", Evolutionary algorithms in engineering and computer science, vol. 2, 1999, pp. 135-161.
[32] G. Mosetti, C. Poloni, and B. Diviacco, "Optimization of wind turbine positioning in large windfarms by means of a genetic algorithm", Journal of Wind Engineering and Industrial Aerodynamics, vol. 51, no. 1, 1994,  pp. 105-116.
[33] S. Rodrigues, P. Bauer, and P. A. Bosman, "Multi-objective optimization of wind farm layouts–Complexity, constraint handling and scalability", Renewable and Sustainable Energy Reviews, vol. 65, 2016, pp. 587-609.
[34] P. Asad Ayoubi, M. Eftekhari Yazdi, and I. Harsini, "A 3D analytical model for predicting horizontal-axis wind turbines wake based on a 2D analytical wake model", Environmental Progress & Sustainable Energy, vol. 41, no. 5, 2022, pp. 500-522.
[35] D. J. Renkema, "Validation of wind turbine wake models, Master of Science Thesis," Delft University of Technology, vol. 19, 2007, p. 590.
[36] P. Mukund, "Wind and solar power systems", 1st ed: CRC Press, 1999.
[37] R. J. Stevens, B. F. Hobbs, A. Ramos, and C. Meneveau, "Combining economic and fluid dynamic models to determine the optimal spacing in very large wind farms", Wind Energy, vol. 20, no. 3, 2017, pp. 465-47
[38] J. S. González, A. G. G. Rodriguez, J. C. Mora, J. R. Santos, and M. B. Payan, "Optimization of wind farm turbines layout using an evolutive algorithm", Renewable energy, vol. 35, no. 8, 2010, pp. 1671-1681.
[39] M. Song, K. Chen, Z. He, and X. Zhang, "Optimization of wind farm micro-siting for complex terrain using greedy algorithm", Energy, vol. 67, 2014, pp. 454-459.
[40] Y. Chen, H. Li, B. He, P. Wang, and K. Jin, "Multi-objective genetic algorithm based innovative wind farm layout optimization method", Energy Conversion and Management, vol. 105, 2915, pp. 1318-1327.
[41] X. Gao, H. Yang, L. Lin, and P. Koo, "Wind turbine layout optimization using multi-population genetic algorithm and a case study in Hong Kong offshore", Journal of Wind Engineering and Industrial Aerodynamics, vol. 139, 2015, pp. 89-99.
[42] J. Hazra, S. Mitra, S. Mathew, and F. Zaini, "3D layout optimization for large wind farms", in 2015 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT) 2015.
[43] A. M. Abdelsalam and M. El-Shorbagy, "Optimization of wind turbines siting in a wind farm using genetic algorithm based local search", Renewable energy, vol. 123, 2018, pp. 748-755.
[44] S. Tao, Q. Xu, A. Feijóo, G. Zheng, and J. Zhou, "Wind farm layout optimization with a three-dimensional Gaussian wake model", Renewable Energy, vol. 159, 2020, pp. 553-569.
[45] K. Balasubramanian, S. B. Thanikanti, U. Subramaniam, N. Sudhakar, and S. Sichilalu, "A novel review on Optimization Techniques used in Wind Farm Modelling", Renewable Energy Focus, vol. 35, 2020, pp. 84-96.
[46] A. Stidworthy and D. Carruthers, "FLOWSTAR-Energy: a high resolution wind farm wake model", Wind Energy Science Discussions, 2016, pp. 1-24.
[47] G. C. Larsen and H. A. Madsen, "TOPFARM-next generation design tool for optimisation of wind farm topology and operation", Renewable Energy Focus, vol. 11, 2011, pp. 71-82..
[48] Y.-T. Wu, T.-L. Liao, C.-K. Chen, C.-Y. Lin, and P.-W. Chen, "Power output efficiency in large wind farms with different hub heights and configurations", Renewable Energy, vol. 132, 2019,  pp. 941-949.
[49] S. Naderi, S. Parvanehmasiha, and F. Torabi, "Modeling of horizontal axis wind turbine wakes in Horns Rev offshore wind farm using an improved actuator disc model coupled with computational fluid dynamic", Energy Conversion and Management, vol. 171, 2018, pp. 953-968.
[50] Y.-T. Wu and F. Porté-Agel, "Modeling turbine wakes and power losses within a wind farm using LES: An application to the Horns Rev offshore wind farm", Renewable Energy, vol.5,2015, pp. 945-955.
[51] J. Feng and W. Z. Shen, "Modelling wind for wind farm layout optimization using joint distribution of wind speed and wind direction", Energies, vol. 8, no. 4, 2015, pp. 3075-3092.
[52] P. Pinson, "Wind energy: Forecasting challenges for its operational management", Statistical Science, vol. 28, no. 4, 2013, pp. 564-585.
Journal of Modeling in Engineering
Volume 20, Issue 70
September 2022
Pages 161-177

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History

  • Receive Date: 21 April 2022
  • Revise Date: 29 May 2022
  • Accept Date: 19 June 2022

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