The placement of wind turbines within a wind farm is crucial for maximising energy output while reducing wake effects (a reduction in wind speed due to energy being extracted by the turbine, leading to a loss in energy generation of turbines behind it) and land usage [1].
Figure 1: Whitelee Wind Farm Turbines.
Traditional methods to determine optimum turbine placement fail to account for the variability and complexity of wind patterns and terrain irregularities. Monte Carlo Simulation (MCS) uses stochastic processes and real-world constraints to optimise turbine placements [2].
The results show that MCS can achieve higher energy efficiency and reduced wake losses compared to other methods. This model is named after the Monte Carlo Casino in Monaco, as its primary developer, mathematician Stanisław Ulam, drew inspiration from his uncle’s fondness for gambling [3].
Monte Carlo Simulation
The Monte Carlo simulation is a mathematical model that relies on random numerical sampling and is used to predict many possible outcomes of an uncertain event and random variables. The MCS framework follows these steps [4]:
- Input Data Collection:
- Wind Resource Data: Historical and real-time data of wind speed, direction, and frequency distribution.
- Terrain Information: Topography, land constraints, and soil conditions.
- Turbine Specifications: Tip Height, Hub height, rotor diameter, and power curve (A graph illustrating the power output of a wind turbine at various wind speeds).
- Random Sampling:
- Generates random turbine layouts within the predefined red line boundary.
- The red line boundary is divided into square cells, with each cell representing a turbine. The model adjusts the location while considering real-world constraints [5].
- Makes sure to follow the minimum spacing requirements and maintain the designated exclusion zones.
- Energy Output Calculation:
- Uses the Jensen wake model or similar analytical models to estimate wake losses [6].
- Computes the net energy output for each of the generated layout.
- Optimisation and Iteration:
- Assesses the performance of each layout in terms of energy output and land usage. Iterate the process to refine the sampling space and converge on optimal solutions.
Conclusion
MCS is a useful tool for optimising the placement of wind turbines in wind farms. By considering random variables and complex constraints, MCS provides a flexible and efficient framework that surpasses traditional methods. One study observed that the model could predict wind farm power output with an error of less than 4% [7]. Future work could incorporate real-time data and machine learning algorithms to further improve the adaptability and accuracy of the simulation framework.
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References
[1] ‘(PDF) Optimum layout design of onshore wind farms considering stochastic loading’, ResearchGate, Oct. 2024, doi: 10.1016/j.advengsoft.2015.05.002.
[2] ‘(PDF) Wind Energy Reliability Analysis based on Monte Carlo Simulation Method’, in ResearchGate, doi: 10.21467/proceedings.4.41.
[3] ‘Hitting the Jackpot: The Birth of the Monte Carlo Method | LANL’. Accessed: Dec. 16, 2024. [Online]. Available: https://www.lanl.gov/media/publications/actinide-research-quarterly/first-quarter-2023/hitting-the-jackpot-the-birth-of-the-monte-carlo-method
[4] R. Liu, L. Peng, G. Huang, X. Zhou, Q. Yang, and J. Cai, ‘A Monte Carlo simulation method for probabilistic evaluation of annual energy production of wind farm considering wind flow model and wake effect’, Energy Convers. Manag., vol. 292, p. 117355, Sep. 2023, doi: 10.1016/j.enconman.2023.117355.
[5] G. Marmidis, S. Lazarou, and E. Pyrgioti, ‘Optimal placement of wind turbines in a wind park using Monte Carlo simulation’, Renew. Energy, vol. 33, no. 7, pp. 1455–1460, Jul. 2008, doi: 10.1016/j.renene.2007.09.004.
[6] ‘(PDF) A Survey on Recent Off-Shore Wind Farm Layout Optimization Methods’, ResearchGate. Accessed: Dec. 16, 2024. [Online]. Available: https://www.researchgate.net/publication/270104991_A_Survey_on_Recent_Off-Shore_Wind_Farm_Layout_Optimization_Methods
[7] S. Brusca, R. Lanzafame, and M. Messina, ‘Wind Turbine Placement Optimization by means of the Monte Carlo Simulation Method’, Model. Simul. Eng., vol. 2014, no. 1, p. 760934, 2014, doi: 10.1155/2014/760934.
Image accreditation: rachelalienergy, CC0, via Wikimedia Commons. Last accessed on 17th December 2024.
